Multiple-Valued Logic, Vocabularies Structure, and Linked List for Data Verification in Dialog Communications of Agents

1. Introduction

Modern research in civil robotics includes at least such fields, see Figure 1, as unmanned logistics and Internet of vehicles (IoV) [1], power grids with smart metering [2], “smart” city [3], autonomous robotic manufacturing [4], Internet of Things (IoT) [5], and medical nursing [6]. The general goal of these investigations, which are based on artificial intellect (AI) concepts of agents and multi-agent systems (MAS), is to imitate human abilities and to design autonomous and self-sustaining large-scale robotic systems, which can operate in wide space-and-time bands without permanent human control. However, the design of autonomous robotic agents is a complicated task, and the development of such systems involves the whole spectrum of conjugated technologies, including the research of modern mathematics [7,8], 5/6 G Internet [9], microprocessors [10], neural networks (NN) [11], fuzzy logic and controllers [12], computer vision [13,14] and speech procession [15], big data procession [16], traditional and post-quantum cryptography [17], quantum key distribution [18], and quantum computing [19]. The design, debugging, and modification of autonomous agents includes autonomous data verification and correction of errors and faults, caused by natural factors or cheaters [18].

The final goal of any type of verification procedures in agents is to exclude possible incidents and crashes caused by faults, attacks and illegal data modifications [20,21,22]. An ideal verification procedure should take into consideration all possible vulnerabilities of agent`s architecture, hardware, and software. It also should take into account current tasks, situation in the scene of action, the trust level of data sources, processed materials, characteristics of objects, and the workload. However, the problem also is to create and support the reliable referent (or template) model for data verification, as attacks can be aimed not only at agents but also at collective resources. Alternative way is to use verification with selective extraction of reference content from the distributed structure of local data storages, using free memory resources in loyal robots and network nodes. Respectively, verification procedure should compare data taken both from internal modules and external data storages, what needs to design the scene description formal model and to use protected from modifications distributed ledgers, partially reproducing the linked list (LL) scheme in blockchain [23,24]. These new options are to complement known data verification methods reviewed further.

1.1. Verification Tasks in Modern Robotics

In the review covering more than 150 papers published in 2008-2018, the analysis was done of formal specification and verification methods for individual and collective robotic systems. The specification was considered as the mathematical description of necessary actions for hardware and software components of the robotic system, which doesn`t determine the method of realization but can verify processes. There were considered many mathematical aspects of the problem, e.g., set–theoretic methods, logic methods of dynamic verification of hybrid systems, temporal logics, timed automata, robots communication languages, agent programming languages, finite state machines, state machines, Petri nets, probabilistic methods, Markov networks, automatic Buhi machines, model verification tools, and ontologies. The review has also covered models of physical environment, certification and trust indicators, external and internal threats. Finally, emphasis was made on the necessity to design integrated formal methods (iFM) for the specification of agent`s tasks, and the enlarging need was accented for the heterogeneous sets of formalisms for complicated systems description, where each one is responsible for its specific component. One more actual problem is the lack of methods to monitor the interrelation between the specification and the executed software code [8]. The authors of review has expressed the hope that the research in this field will help to create Integrated Verification Environment.

The practical realization of heterogeneous sets of formalisms concept and route verification method was demonstrated in for the cosmic robot Curiosity. Other publications has accented the set of actual aspects in formal verification schemes for robotic collectives; among them one should note the peculiarities of constructing both quantitative [26,27] and qualitative [28,29] models. Active research is being held in such fields as predicate systems modelling [26], temporal logic [29,30,31], and epistemological extensions [32]. Also one can see publications devoted to discrete relational models [33], state-based models [31,34], and beliefs-based ones [29]. Good results were obtained with the help of domain-dependent embedded models of Matlab/Simulink [35]. One should note the trend to design dynamic and non-exhaustive verification methods [8].

In the field of verification models for collective robotic systems, the detailed review has also emphasized the following problems:

• too general estimation parameters and the absence of methods to take into account the specifics of domain knowledge,
• the absence of realistic schemes to evaluate the applicability of selected criteria,
• the lack of specialized languages to model domain knowledge,
• insufficient development of methods for runtime verification.

Among other significant gaps, the authors of also has pointed out the lack of real possibilities for quantitative specification, i.e. of ability of known languages to describe the desired properties of the system. However, due to the inhomogeneity of agent`s structure, the languages for robots behavior description should provide as the discrete modelling of dynamic processes, as the continuous one. They are to model stochastic and epistemological characteristics of agents’ interaction with the environment and users. The gap is too large between quantity indicators for intermediate and final tests results. Some other publications also discussed the need for methods to analyze probabilistic and stochastic processes [36], discrete and continuous dynamic processes in agent systems [38]. In paper the emphasis was placed on the fact that namely system description languages should track combinations of stochastic and continuous processes. Very substantial drawback is the lack of public technologies for checks and tests [27,34,40], and complicated systems with the detailed structure description now has no appropriate tools for the model-based testing [35,41] and the run-time verification [31,38]. Basing on content of [8,42,43] one comes to the conclusion, that there is a very small number of developments for industrial verification and specific knowledge domains.

During 2020 - 2024 the interest to practical applications of drones has increased dramatically, and impressive publications have appeared on delivery systems, routing, navigation and verification of real autonomous devices. For example, a method was proposed in for verifying the operation of a drone during task execution, using the knowledge base and rules. An interesting aspect of data protection and routing in delivery drones was touched upon in referring the use of hybrid coding with blockchain components. In a system was proposed for the capturing of illegal drones using a vision and trajectory prediction system. The article discussed the requirement to apply multi-level architecture in the heterogeneous system of agents.

Also agents need combinations of automatic tests and quick visual checks done by human experts. However, neural networks (NN) and deep learning algorithms [49], which already has become the priority tool for computer vision and speech systems [13,14,15], didn`t propose yet new tools for the imitation of human abilities in verification tasks. Moreover, the known problem of NN to make selective data corrections limits the possibility to use NN in verification procedures. Now computer vision systems based on NN [13,14,49] can slowly enough recognize some components of real scenes of action, and can`t detect illegal physical activity of cheaters and rival robots.

As quantum keys distribution (QKD) schemes were realized not only in fiber optics lines, but also in wireless atmospheric data ones [50], they principally can be used for secured robotic communications at comparatively low keys generation rates and short enough distances. Unfortunately, quantum cryptography is too expensive for low data traffic sessions for data verification in MAS.

In order to design multi-parametric verification models, demonstrating scalable description and navigation in the large-scale structure of parameters of network robotics, one can use multiple–valued logic (MVL) modelling based on discrete Allen-Givone algebra (AGA) taken with a large number of truth levels (k>128) [52,53,54]. Earlier there were attempts to use the version of MVL with several truth levels and to realize Kripke structures [55,56,57] for the model checking and modeling of time processes, however that has produced too complicated for practice models. The intricacy here is that representitative graph analysis for all possible transitions of system states is problematic to be used in AI systems with the large number of parameters, noise factors, probabilistic and approximate patterns for the description of people, technical objects, and their faults. But this problem seems to be partially bypassed by the integration of traditional precise, probabilistic, and approximate calculations being held within MVL, Boolean, and fuzzy logic. That determines the choice of the heterogeneous logic architecture of agent [52], which is the tool to simplify joint use of various logic models in multi-parametric modelling. Now AGA can held template matching for pattern recognition tasks and may describe neural network expressions [22]. Fuzzy logic formalisms can be emulated by AGA, which was shown to model the analog of the fuzzy controller with parametric T-gates (or T-norms and T*-conorms) [59]. Basing on quantum random number generators, flexible AGA schemes can model one-time cipher pad secret coding scheme [18], random oracle scheme [60], combined classic and quantum protocols for position-based cryptography [53], and also they gave a pair of algorithms for distant comparison of parameters without their disclosing [59]. AGA verification model provides components of blockchain and the distributed ledger, aggregated in collaborating network nodes [53,54]. All these designs creates new possibilities for the distant data verification in collaborating agents.

1.2. Verification and AI Algorithms in Agents

Distant verification of autonomous agent imposes selective monitoring of the complicated system, imitating dozens of basic human abilities and providing self-sustaining of autonomous functioning, activity and reactivity to external world, ability to communicate, the presence of own goals, beliefs and etc. That is why verification of agent is somewhat a wider task, than the model checking in computing [55,56,57], and it should use many heuristic and semi-empirical methods where the human experts are the final instance. Typical procedures suppose the approval of agent`s authenticity, checks of data integrity, space coordinates confirmation in position-based cryptography, and the verification of passed routes and received licenses [22]. Besides initial debugging, they should include periodic tests, checks after learning and self-learning sessions, upgrade, and data restoration [6,7,8]. One is preferably to include human biometrics of administrators, and such digital “fingerprints” of robots as parts numbers, random paroles, and the prehistory of earlier done work [22]. However, papers reviewed in sec.1.1 didn`t took enough into consideration AI specifics of agents.

Principally, all mentioned above verification methods are to be integrated into some robotic world model (WM) [62], which can be considered as the set of formal expressions currently describing the interaction of robot with objects, selected in the scene of action by the decision–making system. In the presented paper we don`t discuss in details such a global item as the design of WM [62], but suppose to use for its control the heterogeneous logic model of agent [52], combining AGA with traditional Boolean, and fuzzy logic. One of necessary steps here is the design of the joint ordered structure of robotic terminology and the simple communication logic language of agents, which can describe the logic model of the scene of action for different agents and in prospect to involve natural language processing systems [63].

1.3. Network Verification and the Linked List Scheme

Robotic agents from some allocated MAS are supposed to carry out work in a space scene of action, including various individual partner and rival robots, MASs, people, animals, buildings, vehicles, and other objects. All of them are supposed to be recognized by a computer vision system [13,14], LIDAR [64,65], and other sensors. Here for simplicity we don`t consider dashcam videos, which is a useful tool for verification, but itself needs massive AI-based image procession. In order to simplify the modelling of network verification procedures, one should consider several most typical situations, which can occur for a distant robot and are shown in Figure 2. The agent in the allocated MAS can interact with its distant administrator (bot or a man), which is to support distant work of the agent and to verify some of its parameters in a planned mode or for the urgent correction of robot`s behavior. The agent is supposed to exchange any possible communication messages with the administrator (marked by red arrows) and more limited data sets with other agents of the same MAS (shown by yellow arrows), where messages can mainly include parameters of the scene and tasks. The task of data procession here is to provide the logic control for content access, at the same time excluding the transfer of illegal code or confidential information via data channels.

Also, the scene of action imposes the presence of corporative or state regulators with their mobile or static agents, checking licenses, payments, and technical parameters of robots. Agent of MAS should typically exchange with them by several types of formal messages (marked blue arrows) with the limited volume of data.

Verification method should also take into account possible data exchange between MAS and loyal external agents or network nodes, involved by mutual services or a rent. The data flow between agents and external ones (marked by green arrows in Figure 2) can contain requests to send some necessary data, tools, or to write/read notations into the copies of the linked list (LL) or the distributed ledger [66,67,68], which is the distributed protected data storage. Potentially, people in the scene also can communicate with robots concerning positioning, parking and other common problems, which also need special tools for the translation of robotic messages to people and vice versa. Thus, even minimalistic consideration of the scene of action demonstrates the necessity to describe the branched structure of communicating participants and their language protocol.

Also for the efficient interaction with other robots and people an agent is supposed to support and to approve its own trust level (i.e. reputation coefficient) with the help of network “witnesses”, involved into the verification of credentials and authorities. Besides collective resources, possible variant here is to use network low-capacity data storages written in collaborating agents and loyal network nodes, and the further discussion is concentrated on the design of coded vocabularies structure, containing necessary basic terminology for dialog communications and for easy data documenting and extraction by means of AGA-based version of the LL [53,54].

In traditional blockchain scheme [66,67,68] LL prevents illegal data modifications in a group of highly motivated users by sustaining the distributed set of copies in participating network nodes, which are protected by standard tools and hardly can be quickly modified unnoticed by others. In contrast to blockchain, the AGA-based version of LL [53,54] is intended for the collectives of robots and loyal network nodes possessing limited free memory resources. The task here is to “hide” small volumes of critical data, which can later help to detect data errors and modifications. Such resources in agents are considered as hardly accessible ones, as data procession in them is typically optimized for basic operations and only limited data volumes can be periodically extracted by allowed polling procedures.

The formal logic structure of AGA-based LL can be given [53,54] by the function

$${h^{(m,s)}=F}_{ll}\left(m,t,{\mathit{e}}_m,{\mathit{e}}_{m-s}, {\mathit{h}}_m,{\mathit{h}}_{m-s}\right)$$

(1)

where the input variables are the number $m$ and the time stamp $t$, vectors ${\mathit{e}}_{m },{\mathit{e}}_{m-s }$ describe the last and the previous entries, and vectors ${\mathit{h}}_m,{\mathit{h}}_{m-s}$are the approving hash values assigned by verifying network nodes. LL has the logic expression structure $h^{\left(out\right)}$=${p.t.}_1+\dots +{p.t.}_m$, where e.g., the last written entry can be represented as

$${p.t.}_m=h_m^{\left(m,1\right)}\star X_m\left(m,m\right)\star X_t\left(t_m,t_m\right)\star$$

$$\star X_{e,1,m}\left(e_{1,m},e_{1,m}\right)\star \dots \star X_{e,1,p}\left(e_{p,m},e_{p,m}\right)\star$$

$${\star X}_{h,1,m}\left(h_{1,m},h_{1,m}\right)\star \dots \star X_{h,Q,m}\left(h_{Q,m},h_{Q,m}\right)\star$$

$${\star X}_{e,1,m-1}\left(e_{1,m-1},e_{1,m-1}\right)\star \dots \star X_{e,p,m-1}\left(e_{p,m-1},e_{p,m-1}\right)\star$$

$${\star X}_{h,1,p}\left(e_{1,m-1},e_{1,m-1}\right)\star \dots {\star X}_{h,Q,m-1}\left(e_{Q,m-1},e_{Q,m-1}\right).$$

(2)

The simplified scheme of AGA-version LL is shown in Figure 3, where the pre-agreed collective of mutually loyal robots and network nodes is written in the list of participants and creates equal copies of the collectively formed ledger [53,54]. The formal expression structure for AGA-based LL is shown below in Figure 3. Here the first of entries is mixed with the second, and further the second is to be mixed with the third one etc. Thus, LL “mixes” by logic operations random hash values, assigned by external participants, with previous and forthcoming entry vectors $\mathit{e}$. Respectively, MVL version of LL needs some store of quasi random one-time keys [18], preliminary generated by a high quality quantum random number generator QRNG [69]. Like in the blockchain method [66,67,68], data written in the entry can be approved collectively by the majority voting of participants, whose result is considered as the most reliable one. Certainly, the reliability of such data depends on the number of really involved external participants, and for the small one the task is to introduce additional logic mixing of data taken from various internal sources. Respectively, the advanced version of AGA-based LL can additionally mix parameters of internal subsystems of the agent with external data and assigned hash values.

In order to use AGA–based LL on practice, it is necessary to overcome several obstacles. The first of them is to create the control scheme to support the necessary structure of robotic requests and replies (considered together they are called entries), taking into account the structure of internal modules in various agents. Another challenge is to combine automatic and human checks [63]. One more unsolved problem is to prove that no messages were lost, illegally deleted, or added by cheaters. The last opportunity somewhat intersects with the detection of attacks “man-in-the middle” [70], but in contrast to cryptography now the aim is to prevent data modifications and to imitate human ability to analyze content in the intermittent dialog.

Both version of AGA-based LL [53,54] are oriented at such practical tasks as:

• approval of requested numbers of licenses and permissions,
• following to restrictions declared for cargo parameters and route passing,
• monitoring of visits only to legal zones of the geographical map,
• loading/uploading in legal terminals,
• compliance with the standards of ecology and transport.

1.4. The Aim of the Paper

The goal of this paper is to:

• widen the spectrum of AGA-based data verification algorithms for agents by the holistic vocabulary structure of terminology and its logic coded variables;
• simplify and unify verification schemes by AGA-based communication language, convenient for dialogs of agents in extendable large-scale robotic system;
• adapt the LL scheme to local data storages in network agents and to messages integrity checks;
• provide the clear control of verification schemes in the heterogeneous logic architecture of agent.

Further sec. 2 contains MVL basic mathematical tools, sec.3 proposes AGA representation of the vocabularies structure and the communication language, sec. 4 is devoted to adapted verification schemes based on LL, and sec. 5 presents the fragmentation scheme of AGA functions for human checks. Sec. 6 discusses microassembler modelling and supporting platform. Sec. 7 discusses further research.

2. Method: Basic MVL Model

According to earlier proposed heterogeneous logic model of an agent [52], AGA is considered as a tool to design multi-parametric logic model for the description of the scene of action and verification procedures.

2.1. Multiple-Valued Allen-Givone Algebra

As in earlier publications [52,53,54], we consider basic definitions of MVL according to [51], where the discrete $K$-valued Allen-Givone algebra (AGA), operating with discrete MVL functions $y=f\left(x_1,\dots ,x_n\right),$ is given for $n$ input variables $x_1,\dots ,x_n$and one output variable $y$. It is very handy for multi-parametrical modelling in AGA, that variables and an arbitrary function $y=f\left(x_1,\dots ,x_n\right)$ can have $K$ discrete truth levels from the finite set of natural numbers, i.e. $x_1, x_2 ,\dots ,x_n ,y L=\{\mathrm{0,1},\dots , K-1\}$. Here 0 respond to the absolute false value and $k-1$ indicates the absolutely true one. The complete set of AGA operators given by exp.(1) guarantees the representation of an arbitrary logic function

$$<0, 1,\dots , K-1, X\left(a,b\right), ,+>$$

(3)

$$y=f\left(x_1,\dots ,x_n\right) \text{by some combination of}$$

• logic constants $0, 1,\dots , K-1$,
• operators Min($x_i,x_j$) or$\wedge$, marked by $,$ select the minimal truth level in the pair $x_i$ and $x_j$,
• operators Max($x_i,x_j$) or $\vee$, marked by + , select the maximal truth level in the pair $x_i$ and $x_j$,
• operators Literal $X(a,b)$ given by exp. (2):

  $$X\left(a,b\right)=\left\{\begin{array}{c}0,if b<x<a\\ K-1,if a\le x\le b\end{array}\right.$$

  (4)

  where always $b\ge a,$ and $a,b\in L=\left\{\mathrm{0,1},\dots ,K-1\right\}.$

2.2. Possible Discrete Scales for Mapping of Truth Levels

All truth levels in AGA, see Figure 4 (a), are to be processed and compared according to the scale$0, 1,\dots , K-1,$ [51], which belongs to the class of lattices, where all levels are comparable. But principally, MVL may be given differently, e.g., in [56,57] the 6-level logic was defined with two non-comparable elements “don`t know “ and “don`t care “ for the scale shown in Figure 4 (b). Such model was designed for model checking by means of temporal logic and Kripke diagrams [56], and in fact it included both positive and negative estimations of truth levels. However, in other papers of these authors`s this system has given complicated and non-visual method of checks. In contrast to it, the proposed further method is intended for the heterogeneous logic architecture of agent based on AGA and uses simple scale with the large number $K$ of all comparable truth levels. It can exceed 256 ones and may use the full capacity of standard 8-16-32-64 bitmemory registers for the emulation by microprocessors [72]. Here the axis with truth levels is the scale for mapping of various subsets of physical and model parameters, and we interpret the truth level as the ordered affiliation of different variables and corresponding mapped objects to the holistic agent`s model, as well as the tool to classify parameters. Involved logic parameters may respond to incomparable physical properties (e.g., red and triangle), which should be described by various logic variables mapped of the truth scale given in Figure 4 (b). Principally for wide-band space systems or long-term time control one can use nonlinear mapping onto the scale of truth levels, thus complementing the method of correlated variables discussed in sec. 2.4.

2.3. Formation of AGA Functions

For holistic or fragmented MVL modelling one should use traditional and universal representation of MVL function by the truth table shown in Table 1. MVL function $y=f\left(x_1,\dots ,x_n\right)$ has the overall number of raws $K^n-1$ in contrast to Boolean logic with its only $2^n-1$ rows. The column for the output variable $f\left(x_1,\dots ,x_n\right)$ should be filled in by logic constants $C=\{0, 1,\dots , K-1\}$ according to expert choice or some formal model. Every row of such truth table with the nonzero value of the output variable $F\left(\dots ,\dots ,\dots \right)$has equivalent representation by a product term [51], written via logic constants and operators from exp. (5).

The overall logic expression is given by exp. (5):

$$\begin{gathered} y=F(\mathrm{0,0},...,0)*X_1\left(\mathrm{0,0}\right)*X_2\left(\mathrm{0,0}\right)*... * \\ {X}_n\left(\mathrm{0,0}\right)+ \\ +F\left(\mathrm{0,0},...,1\right)*X_1\left(\mathrm{1,1}\right)*X_2\left(\mathrm{0,0}\right)*... * \\ {X}_n\left(\mathrm{0,0}\right)+ \\ \dots \\ +F(K-1,K-1,...,K-1)*X_1(K-1,K-1)*X_2 \\ (K-1,K-1)*... *X_n(K-1,K-1). \end{gathered}$$

(5)

Here indexed Literals $X\left(\dots ,\dots \right)$ are written by $X_j\left(q,q\right)$and filled in by equal parameters $a=b=q$, where $q$ values are taken from the corresponding row of the truth table. For memory storage and calculations, AGA functions can be equivalently represented by matrixes exp. (6), formed by logic constants $C=\left\{0,1,\dots ,K-1\right\}$ and describing values of the output variable $F\left(\dots ,\dots ,\dots \right)$ and indexed pairs of Literal parameters ($a_i,b_i), i=1,\dots ,n$:

$$A=\left(\begin{array}{ccc}{a}_{11}& \dots & a_{1n}\\ \dots & \dots & \dots \\ a_{K^n-\mathrm{1,1}}& \dots & a_{K^n-1,n}\end{array}\right),B=\left(\begin{array}{ccc}{b}_{11}& \dots & b_{1n}\\ \dots & \dots & \dots \\ b_{K^n-\mathrm{1,1}}& \dots & b_{K^n-1,n}\end{array}\right), C\left(\begin{array}{ccc}{c}_{11}& \dots & c_{1v}\\ \dots & \dots & \dots \\ c_{K^n-\mathrm{1,1}}& \dots & c_{K^n-1,v}\end{array}\right)$$

(6)

Here always${\mathit{b}}_{\mathit{i}\mathit{j}}{\mathit{a}}_{\mathit{i}\mathit{j}}$, n - is the number of input variables, $\mathit{K}$– is the number of truth levels. The switching function in AGA guarantees the reproducing only of data written in its truth table or in equivalent logic expressions, and can output error only if it was illegally or not correctly modified.

2.4. Correlated Variables for the Description of Large-Scale Space and Time Bands

Mobile agent should imitate human ability to estimate time, space, light intensity, and some other parameters in wide bands of values and with various precision (e.g., from micrometers to thousands of kilometers). In order to obtain wide range of measurements, to avoid too large number of truth levels $K$, and to use more cheap hardware, one can use the method to combine in one AGA logic expression data, describing the same physical parameter with various precision of data in the same function. Then the description of e.g., position$x$ =2830 m for the space axe $[0,x)$ can be represented in the digital map as $x=2 km+800 m+30m$ and written by an expression like $x=x^{\left(1\right)}\times 1+x^{\left(2\right)}\times 10+\dots x^{\left(p\right)}\times {10}^p$. This expression can be represented in the MVL truth table with any necessary precision as a set of $p$ correlated input variables $x^{\left(1\right)},x^{\left(2\right)},\dots {,x}^{\left(p\right)}.$ Such variables should be processed as ordinary logic variables in the multi-parametric AGA function [52], but only the summation of the whole set of used correlated parameters provides correct restoration of physical distances. This step should be monitored in methods described in sec. 3 and 4 for forward and backward mapping between truth levels representation and natural numbers one.

For description of various systems, one can freely exploit correlated variables together with ordinary ones, and there is no necessity to insert all defined correlated variables ${\mathit{t}}^{\left(k\right)}={\{t}^{\left(1\right)},\dots ,t^{\left(K\right)}\}$ into all used functions, as namely the shortened set of correlated variables is convenient for human or quick automatic checks. If necessary, e.g., for monitoring of 2D space maps, one can use input space variables ${\mathit{x}}^{\left(i\right)}=(x^{\left(1\right)},\dots ,x^{\left(I-1\right)})$, ${\mathit{y}}^{\left(j\right)}=(y^{\left(1\right)},\dots ,y^{\left(J-1\right)})$, and time variables ${\mathit{t}}^{\left(k\right)}={(t}^{\left(1\right)},\dots ,t^{\left(K-1\right)})$ in a separately defined MVL function $F\left({\mathit{x}}^{\left(i\right)},{\mathit{y}}^{\left(j\right)},t^{\left(3\right)}\right) ,$which

may describe time processes ranging from nanoseconds in microcontrollers up to months in a logistic navigation system for the description of visits to cargo terminals.

However, the use of correlated variables has some restriction disclosed by the Figure 5 for the correlated space variable $x^{\left(l\right)}$. The excessive number of chosen correlated input variables $x^{\left(l\right)}$ will finally lead to the situation, when the resulting measurements and the statistical error will achieve the given difference between two neighbor truth levels. Then according to the theory of physics measurements [72], both truth levels are possible within the given confidence interval, and AGA model then should add two new product terms $C{*X}_x^{\left(l\right)}\left(a,b\right)*\dots$with logic constants $C$ equal to 1 and 2. This contradicts to the principal of AGA modelling of control systems, which needs bijective mapping of physical and logic values for forward and reverse interpretation of data. Such ambiguity can lead to errors and needs to shorten the excessive number of correlated variables in case (b); this restriction should be taken into account at least for space coordinates, time, and laser beam intensity. AGA calculus hasn`t embedded tools to check such data, and the designer should do this himself.

3. Results: AGA Logic Variables for Scene Description and Dialog Communications

Further the method is proposed to describe robotics scene of action and dialogs of agents within the discrete logic calculus AGA, using the large number of discrete truth levels k ≥ 256 [18,52,53,54] and the ordered structure of coded vocabularies containing selected basic terminology. Partially it dates back to ontology methods reviewed in [8].

3.1. Representation of the Scene of Action by Natural Language, Numerical Codes, and Truth Levels

According to sec. 1.3 we consider the agent and its MAS within some scene of action (see Figure 2) containing various partner and rival participants. Necessary definitions are given in Table 2. It considers the set (or the total vocabulary) $V^L$ of all different robotiс terms, given by words or their collocations selected by knowledge experts. These vocabularies should describe all input and output variables used in model functions.

One should note, that the code word may mean action, tool, some equation, and subroutine for calculations of robotic work parameters. Total vocabulary can be preliminary selected by library services and processed by experts [73]; here we omit possible problems for the translation from one language to another one. The selected collection of necessary terms $V^L$ is to be subdivided into subsets $V_v^L$, describing robotic tasks, actions, and tools by various word classes (noun, verb, adjective, cardinal numbers etc.). Then we should represent all these terms by unique natural numbers codes written in vocabularies $V_v^N$. This intermediate coding is necessary for convenient grouping of terms and verification procedures. Further one should map these number codes onto the discrete scale of truth levels $K$ defined in AGA. Corresponding structure of mapping is shown in Figure 6.

The specifics of mapping to $V_v^K$ in Figure 6 (a) is that we can arbitrarily or randomly assign truth levels to words in order to obtain convenient for the classification groups of terms [52], as the simplification (and shortening) of AGA expressions is based on consensus method of minimization [51], which ranks and forms logic product terms according to logic constants. Substantial feature of the used subsets $V_v^L, V_v^N, V_v^K$ is that the number of elements in them is less or equal $K$, and unused vacancies in subsets are to receive zero values. Mappings $V^L$→$V^N$and$V^N$→$V^K$ are bijective, i.e. each element of a subset maps to only one of elements in another subset, what provides simple forward and backward translation by transcoding tables. Chain mapping scheme is disclosed by Figure 6 (b) and responds to sequential clarification of content by the finite chain of conjugated vocabularies $V_{1,m}^L\to V_{2,m}^L\to V_{3,m}^L\dots \to V_{K,m}^L,$ where $V_{1,m}^L$is a root vocabulary. Such method is to provide the unified protocol both for robots with simplest and advanced hardware platforms, where the first part of the message can contain coded words written closer to root vocabularies and the actuality of information can be quickly estimated by all agents, even capable only to partially interpret the message. Also agents can undertake some actions immediately, before the transfer of all details.

The formation of content root vocabulary $V^L$ is given in Table 3, which describes words of natural language. Every term (or word combination) of natural language is included into some vocabulary. Every vocabulary $V_{v,m}^L$ contains up to $K$ different words $w_{v,m}^{.L}$. Numbers $N=1÷M$ refer to root vocabularies. Values $N$ from $K+1$ up to $2K$ refer to the second one in the chain mapping of vocabularies.

The first field in Table 3 is the initiation (or welcome) word of dialog, also indicating the type of communication format for messages and the number of parts of the phrase, which may differ for various sectors of robotics. The name description of addressers and senders may use matrix $V_{v,m}^K$ with chain vocabularies and several bytes for microprocessor representation of participants, but for brevity only two chain vocabularies $V_{v,2}^K$ are shown in the Table 3; their common matrix is defined by two parameters$v,m \le K$. For simplicity, further we avoid (where possible) to use the third index for the description of the number of a word in the specific vocabulary. The order of numbering in vocabularies $V_{i,j}^L$is not substantial. Every tool and identified object in the scene of action can have only one name. Note e.g., that the time of action $w_7^K$ (from $V_{\mathrm{1,7}}^K$ in Table 3) can be taken with symbolic values “immediately” or “urgent”.

AGA modeling of the scene of action is based on three equivalent representations of vocabularies $V_{v,m}^L\to V_{v,m}^N\to V_{v,m}^K$ shown in Table 4. The parallel use of natural language, natural numbers code and truth levels naturally occurs when one firstly tries to explain the work of the designed robotic system, and after this turns to numbers codes and AGA models. Such rigid binding of variables representations is convenient for human experts.

Correlated variables can be written to Table 4 as a sequence of $w_{i,g,k}^K$, sequentially raising the precision of space coordinates but following the restriction from sec. 2.4.

The scheme of logic transformations between natural numbers code and truth levels ones is given in Figure 7, which shows the initial mapping of $w_{i,j}^N$data onto the logic representation $w_{i,j}^K$, and further the reverse mapping to natural numbers, as arithmetic check coefficients calculations are to be done within Boolean logic. For further convenient procession, the maximal logic value $K-1$ and its natural numbers equivalent are reserved for possible minimization procedures in AGA. By default, zero value indicates the not used word in a vocabulary. Check coefficients $C_{i,j}^N, C_{i,j}^K,C_{i,j}^{NXR}$,$C_{i,j}^{KXR}$ are to be calculated within the mapping of AGA to natural numbers scale (see sec. 3.3).

Verification procedures can involve two data input channels with truth level codes and natural numbers ones shown in Figure 8 (a). It can include procession and comparison of data coded as in truth levels, as in natural numbers codes. Independent coding of these two channels gives the principal possibility to compare separately final and intermediate results and to detect errors or illegal modifications of data, as final results in both representations should be the same or close, if approximate estimations were used. Also equivalent representations are considered as the binding tool for the heterogeneous logic architecture of agent [52], which supposes parallel calculations in various logic models.

At the same time, natural numbers code and AGA truth levels representations have different numbers profiles for comparison. Figure 8 (b) shows the principle of brief verification procedure for used vocabularies in the agent. Besides this, visual representation by histogram shown in Figure 8 (b) is more convenient for human checks. Within the proposed scheme of vocabularies, known types of activity and coded tasks execution should lead to preliminary known set of vocabularies describing controllers and actuators. Independent checks may be held both in vocabularies $V_{v,m}^N$ and $V_{v,m}^L$. As AGA truth levels representation $w_{v,m}^K$ is compatible with the secret data coding scheme and the scheme for distant comparison of data without their disclosing [53,54], namely it is preferably to be used for the control of data access in agents. Natural numbers codes $w_{v,m}^N$ are better to be used for common access content and less confidential data. Full check of the agent will need comparison of all words $w_{v,m}^K$ and $w_{v,m}^N$ in used matrixes $V_{v,m}^K$and $V_{v,m}^N$. However, all such procedures need one more critical component.

and further chain ones.

3.2. Communication Phrase

There exist formal theories of language construction like considered in [74], although modern natural language procession systems typically use Chat GPT and NN [75]. However, earlier the simplest AGA-based scheme of the communication protocol was proposed in for secretly coded instructions transfer via the wireless laser data line λ $=0.63$ μm with pulse-width-modulation. This scheme has used the fixed position of several specialized vocabularies in the phrase $\mathit{W}$ and was intended for 8-bit microcontrollers platforms. The small number of internal memory registers in them has limited the transfer of short phrases given by the format {Sender of message - Receiver of message - What to do - Where to do - When to do - Commentary for next phrase}, coded by 8–bit numbers. This earlier version of protocol corresponds to the shortened sampling taken from Table 3 for the particular set of vocabularies:

{$V_2^L$(Sender of message) $-V_3^L($Addresser of message)$-V_4^L($Task)$-V_6^L($Place of action$-{V_{13}^L\left(\mathrm{T}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{o}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\right)-V}_1^L\left(\mathrm{F}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{n}\mathrm{e}\mathrm{x}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{a}\mathrm{g}\mathrm{e}\right)\}.$However, now the task is to propose the flexible and unified 8-16-32-… phrase format, adaptable to various tasks and the large number of vocabularies. Also, such format should help to find correct parts of phrase and to determine lost ones which are to be repeated. Additional requirement is to use independent microcontroller data channel for dialogs, providing enough content transfer but using rigidly given protocol, excluding uncontrolled intrusion of external code into the software of agent.

The necessary structure of the phrase vector${\mathit{W}}^{\mathit{K}}$, describing the robotic message, is given in Table 5. Every phrase is a fragmented one and contains the addressing header and content parts. Their length is 8-bytes what is accessible for cheap 8-bit platforms, and the overall length of ${\mathit{W}}^{\mathit{K}}$ principally can be enlarged up to $K$ parts, but is supposed to be typically limited by 2-8 ones. Components of vector ${\mathit{W}}^{\mathit{K}}$ are the elements of various vocabularies given in Table 3 and Table 4. Principally, alternative representations by words$w_{v,m}^N$also can be used in phrases, but in this paper we don`t use them. Parts of phrase shown in Table 5 can be transmitted separately and afterwards may be assembled into holistic phrases with the help of hash values and total check coefficients. That excludes the possible problem of time delays for multi-channel data aggregation.

The header part includes obligatory fields “Format”, “Fixed parole”, “Addresser”, and ”Sender” with the fixed position in the phrase for the quick and simple procession. Priority of position of root and other vocabularies in the phrase is given by the field “Format”. The value$w_{\mathrm{1,1}}^K=“\mathrm{Hi}$” may be given by several various numbers, initiating the new dialog and indicating at the same time the number of content parts. The field “Fixed parole” is intended for the initial access of preliminary allowed agents and includes words taken from the vocabulary $V_{\mathrm{1,2}}^K,$ which contain fixed passwords for initial contact only. Further communication modules of Sender and Addresser should assign quasi-random hashes to content parts of the phrase. Respectively, every content part also includes obligatory field “Hash”, describing assigned one-time quasi-random hashes, necessary for correct integration of transferred parts into the holistic phrase. This field should use preliminary stored reserve of random keys, obtained from external QRNG or random oracle scheme [60]. Such one-time access keys e.g., also were envisaged by AGA protocol for confidential distant comparison of parameters without their disclosing [59]. Fields “Arbitrary code word,$w_{v,m}$” in сontent parts of the phrase are to be filled in by arbitrarily chosen words, forming some sampling $K^{`}$ of logic variables, where $K^{`}\le K$. The maximal number of content parts $j$ in the phrase is determined by the expression

$$j=N_{usedvocab.inphrase} – N_{usedinheader}/N_{freefieldsincont.part}=(KxM-4)/N_{freefieldsincont.part}$$

(7)

Format of messages shown in the Table 5 certainly can be further adapted for a specific knowledge domain, a large number of participants, and for large space and time bands of work. E.g., for extraordinary situations like a fire, any robot should have reserved code word in the field “Format” for the activation of chain vocabularies, describing phrases like {Fire service - Fire department q - Fire robot qq-….} and {City q – Municipal district qq - Street qqq-…}. But for routine tasks the long chain of vocabularies can be excessive.

Total check coefficients$C^K$ and $C^N$ shown in Table 5 need special commentary, as they suppose arithmetic summation of words codes for messages integrity verification. Such verification procedures for a noisy data line can determine, if some parts of the phrase were modified, added, or losted due to noise or intruders. This method suppose summations of codes for all used indexes $v,m$ and parts of phrase. As the summation is not initially defined in AGA and one can`t directly use Boolean calculations for the set of truth levels data, words codes should be preliminary mapped onto the scale of natural numbers $N$ before traditional arithmetic calculations. Results of calculations should coincide for sums obtained by Addresser and Sender. For 8-bit microcontrollers with embedded arithmetic procedures this check unavoidably uses the summation with case overflow, what provides the independence of verification parameter from the number of actually used words and transmitted parts of the phrase. Besides this, in such scheme well-known binary operations XOR used in may be also applied for the detection of permutations of words in a phrase and parts of the phrase. In order to use such verification schemes, one should make several definitions.

Definition 1:

Total check coefficient$C_i^K$of mapped truth levels is given for a phrase${\mathit{W}}_i$written in AGA logic codes and is the arithmetic summation$C_i^K=$ ${\sum }_v^{K`}{w}_v^K$, carried out within Boolean logic for truth values of all words$w_v^K$, used in the phrase${\mathit{W}}_i$and given by arbitrary sampling of vocabularies$V^{K`},$ $K` K.$AGA truth levels before summation are mapped onto the linear scale of natural numbers N.

Application of the def. (3.1) is supposed to be convenient both for independent human checks and for automatic comparison with template data.

Another convenient coefficient for checks is given by Definition 2.

Definition 2:

Total check coefficient$C_i^{N/K}$of arithmetic summation of natural numbers codes is given for a phrase${\mathit{W}}_i$written in mixed natural numbers and truth levels codes and is the arithmetic summation$C_i^{N/K}=$ ${\sum }_v^{N`}{w}_v^{N/K}$, carried out for natural number codes and mappings of truth levels codes of words$w_v^N$or$w_v^K$, used in the phrase${\mathit{W}}_i$and taken from the sampling set of vocabularies$V^{N`}$and$V^{K`}$,$N`,K` N.$

Coefficient $C_i^{N/K}$ is necessary for human or automatic checks within the heterogeneous logic architecture of agent, where one can independently visualize natural numbers codes and evaluate the integrity of the dialog data exchange$\mathrm{b}\mathrm{y}$ the summation of all values $w_v^N$ in the phrase.

One more useful tool for the logic verification in agent is the well-known Boolean logic operation XOR, used for the set of words in the phrase ${\mathit{W}}_i$ represented by truth levels or natural numbers code. Its destination is to make digital “fingerprints” for phrases and their parts. XOR operation can help to compare identity and to hide real codes used in sessions held even without secret coding.

Definition 3:

Total coefficient $C_i^{XRK}$of check XOR binary logic operation taken for mapped truth levels is the set of Boolean XOR operations$C_i^{XRK}=$ $\widehat{w_1^K}\dots \widehat{w_{K`}^K}$carried out in the phrase${\mathit{W}}_i$for binary representation of AGA truth levels of words$\widehat{w_v^{K`}},$mapped onto the linear scale of natural numbers N.

Definition 4.

Total coefficient$C_i^{XRN}$ of check XOR binary logic operation is the set of Boolean XOR operations$C_i^{XRN}=$ $w_1^N\dots w_{K`}^N$carried out in the phrase${\mathit{W}}_i$for binary representation of natural numbers codes of words$w_v^{K`}$.

One should note, that coefficients Def. 1÷4 also can be easily used in phrases ${\mathit{W}}_i,$ transmitted by parts, like as it is shown in Table 4. “Sewing” or ordering of parts of the phrase ${\mathit{W}}_i$ in the addresser agent supposes the check of coefficients Def. 1÷ 4 as for whole phrases, as for their separate parts. The only necessary complication here is to insert separately calculated coefficients in the end of every phrase part (see Table 6), and every time to fill in the total sum for all parts from the very beginning of the phrase, including the header. The specifics of coefficients Def. 3÷ 4 is that they are intended for more confidential data or for work in the tense media, when the increased level of caution is to be activated in the MAS.

The detection of lost and mixed content parts during the transfer of phrases in dialog mode can be based on the check for assigned one-time hash values and the comparison of data, obtained by the summations of coefficients $C_{i.j}^K$. The example of such algorithm is given in sec. 3.3. Besides this, for vocabularies$V_{v,m}^N$, where$v\left\{1,\dots ,K\right\}, m\left\{1,\dots ,M\right\}, M\le K$, one can apply coefficients$C^N$and$C^{NXR}$, taken in natural numbers representation$.$

3.3. Communication Module and the Dialog Protocol

Procession of dialog messages is considered further only within the specialized communication module, but for correct design of verification procedures it is necessary to discuss briefly its interaction with other agent`s components. The very simplified interpretation scheme of agent and its basic work cycle is shown in Figure 9, although its internal modules can include additional internal feedback contours and auxiliary data lines. Any realistic autonomous mobile robot should include:

a) sensors and computer vision system, which are to detect objects and dangers, providing the agent`s reactivity to the external world and space positioning;

b) module for the procession of messages, coming from radiofrequency, acoustic, and optics data lines, complemented by devices for secret coding and data verification;

c) homeostasis supporting system [79], providing autonomous operation of devices for energy supply, time clocking, sensors operability control, and space positioning;

d) modules for decision making and work planning;

e) set of actuators.

Principally, one of main properties of agent is to follow the principle of the so-called homeostasis in biological systems and to support autonomous work of a robot by self-sustaining of appropriate bands of “vital” parameters, like alive systems support concentration of oxygen and glucose in blood using the cyclic principle of work and control contours with feedback. Using internal subsystems, the agent executes received tasks and instructions [79], what somehow changes the external media. Agent sequentially monitors these changes by its sensors and repeats the work cycle, thus realizing closed contours of control with the feedback obtained via the external media. Such cycles can involve time bands varying at least from nanoseconds up to months, what needs to use correlated time variables. That is why the universal communication module of agent and verification procedures should model the detailed structure of parameters, and it can`t be limited by several verification templates.

The receiving messages agent is to take into account instructions transferred by the administrator and requests from other agents, what may quickly change states of the homeostasis contours. Only after this the agent is to activate decision-making procedures, which may cause series of actions and need various run time. As embedded modules of agent suppose somehow optimized mode of work, the realistic way is to run verification procedure after the completing of the next work cycle [59].

If some agent receives the initiating signal in a new phrase, the dialog scheme of two agents can include a vast spectrum of procedures and AI algorithms as follows:

• to check the received initial parole in the list of fixed and additionally generated ones;
• to extract potentially danger data to be immediately send to homeostasis module,
• to check the presence of the declared sender name and its authority in the AGA function, describing allowed classes of actions for the contacting agent,
• to verify the presence of all declared content parts in the received phrase;
• to compare the requested by external agent set of vocabularies and the allowed one;
• either to begin the new dialog, or to continue the already opened one; if necessary, to send denial reply;
• to send content of the received phrase to the decision-maker and to wait its reply;
• to work out the reply phrase and to assign to it a one-time random hash value, using the reserve list of hash values preliminary filled in by quasi random numbers;
• to add new entry into the LL of incoming messages to save the history of joint work;
• to analyze the reason of errors in the dialog and to choose adequate actions.

The proposed further scheme of dialog communications, combining AGA control of vocabularies and the binary calculation of total check coefficients, bases on Table 3 and Table 5 and is given in Figure 10. During the dialog exchange of messages between agents within the same MAS we don`t make the difference between Administrator and Agent of MAS, although the first one should have additional data channels. All phrases ${\mathit{W}}_{ij}$ are subdivided into initiating dialog requests and replies to them.

According to Table 5, all phrases in the request and reply messages include the header with obligatory several fields and content parts. Indexed values $w_{ij}$ define some sampling of words, chosen from the corresponding set of vocabularies by the communication module and the decision maker. External communication module of administrator and agents adds hash value, which can be either fixed initial access password $w_{\mathrm{1,2}}$, or further assigned quasi random hash value $w_{\mathrm{1,3}}$=$h_{ij}$, which for better reliability should be obtained from cryptographic hash functions or QRNG [69]. In Figure 10 it is supposed, that the communication session is a new one, and Sender of the phrase initiates the dialog, so that the first field “Format” in the header of phrase should contain initiation word $w_1^K$ =“Hi”. It activates further the input of initial access parole $w_{\mathrm{1,2}}^K$ written in the vocabulary$V_{\mathrm{1,2}}^K$. This set (or list) of fixed passwords is intended for the new sessions initiation only, as during the current communication session interacting agents should add one-time hash values taken from the preliminary generated list $L_{hash}$. Other components of the header of the phrase ${\mathit{W}}_{11}=\{w_{\mathrm{1,1}}^K,$ $w_{\mathrm{1,2}}^K,$….} are the triples ${(w}_{\mathrm{1,4}}^K,w_{\mathrm{2,4}}^K,w_{\mathrm{3,4}}^K$) and ($w_{\mathrm{1,5}}^K,w_{\mathrm{2,5}}^K,w_{\mathrm{3,5}}^K$), describing all given Addressers and Senders. Such 8-bit triple can support 16 777 216 agents.

The phrase procession scheme shown in Figure 10 corresponds to Algorithm 1, which is given in Appendix A due to its length. It describes the overall scheme of formal checks of initiating words, passwords, check coefficients, search of the header and content parts, and the waiting of reply in the dialog mode.

Table 6 demonstrates the numerical example of the phrase, disclosing the scheme to find correct content parts in the buffer using the header part. As besides the correct content part the receiving buffer of agent potentially can contain by a mistake some excessive illegally sent parts or ones, taken from someone else’s message. Its analysis is based on simple summation of mapped truth levels and the comparison of total check coefficients, obtained by Addresser and declared by Sender.

The simple scheme to select correct content part of the phrase in the buffer memory, containing several ones, is given in Algorithm 2.

Algorithm 2. The procedure to find correct content part, corresponding to the given header, basing on check coefficients.
Input:	${\{ w}_{\mathrm{1,1}}^K$,$w_{\mathrm{1,2}}^K, w_{\mathrm{1,4}}^K$,$w_{\mathrm{2,4}}^K,w_{\mathrm{3,4}}^K$,$w_{\mathrm{1,5}}^K$,$w_{\mathrm{2,5}}^K$,$w_{\mathrm{3,5}}^K$}, ${\{ w}_{\mathrm{1,3}}^K$,$w_{v,m}^K, w_{v,m}^K$,$w_{v,m}^K,w_{v,m}^K$,$w_{v,m}^K$,$w_{v,m}^K$,$C^{N/K}$}, ……….. (up to 30 parts in the buffer)	← Header ← Content parts
Step	Procedure		Example from Table 6
1.	Find header part of phrase in the buffer memory		-
2.	Calculate with 8 bit overflow $C_{header}^{N/K}$ for the header		$C^{N/K}=$138 (< 255)
3.	Find nearest content part		-
4.	Calculate with 8 bit overflow $C_{cont}^{N/K}$ for the content part		209+196+3+12+6+221+147= 794(overflow: >255)== 794-3x255=29;
5.	Calculate with 8 bit overflow:$C_{header}^{N/K}$ +${ C}_{cont}^{N/K}$		138+29=167 (< 255)
6.	Compare, if the calculated result is equal to the declared one in the last field of the content part:$C_{header}^{N/K}$ +${ C}_{cont}^{N/K}$ =$C_{header}^{*N/K}$ +${ C}_{cont}^{*N/K}$ ;If yes, then write header and content part in the buffer;other, then find and process next content part.		-167=167yes
Output:	→ Correct pair of header - content part of phrase is in the buffer

The further procession of the received phrase ${\mathit{W}}_{i,j}$ should include the check for compatibility of allowed tasks and vocabularies, mentioned in the request. The detailed analysis of this vast topic is out of this paper, only several remarks are to be given. The aim here is to detect incorrect content messages and to limit the access of robots to currently not allowed topics and knowledge. That needs to design special AGA function, which in general case should take into account the current state of the scene of action and the dynamics of its development. Respectively, this procedure needs to additionally estimate such control parameters as e.g., the level of danger $d$, trust level $tl$, and level of available resources $r$. The multi-grade parameter “danger level” may be varied by an administrator, computer vision system, and sensors, what differs it from the “trust level” one, which supposes long enough monitoring of behavior of objects in the scene of action. This variable together with the trust level seems to use the simplified discrete structure of AGA truth levels with 5-10 grades, but the estimation of them may need probabilistic calculations. Resources data (like batteries charge voltage) can be united in one final logic variable, but complex planning algorithms may be needed to estimate the possibility to carry out the task. Thus, the principle of multiparametric AGA logic phrase procession is simple enough, but realistic robotics needs to add many expert data. Some of them are preferably to be written as templates for verification and should be protected from illegal modifications by the adaptation of earlier proposed schemes of AGA-based LL [52,53].

4. Results: LL Adaptation for Dialog and Verification Procedures

If verification and data restoration procedures are not supposed to be often held, massive dubbing of all incoming and sent messages by copying or AGA-based LL [52,53] seems to be appropriate mainly for administrator`s archiving, possessing substantial resources. Respectively, it seems reasonable to use shortened adaptations of AGA version of LL especially designed for messages aggregation and completed work history documenting. Such confidential data structure should contain brief information concerning earlier carried out tasks which may be confidential enough. The task to avoid illegal data modifications undertakes the problem of often repeated values of words $w_{v,m}^K$, necessary for typical robotic tasks, where even the space localization of a robot prompts most probable combinations of used in dialog words. LL schemes can additionally include total check coefficients ${ C}^{K/N}$ (using summation of mapped truth levels) and ones $C^{KXR}$ (using binary XOR operations). Such total coefficients for parts and whole phrases complicate the external prediction of instructions for frequently repeated tasks. Also one can periodically change the coding for truth levels representation, and for situations with the high risk of illegal activity of cheaters one can exploit standard NIST techniques of secret coding and AGA-based analog of the well-known one-time cipher pad scheme [18].

The problem to be solved here is that AGA versions of LL [52,53] initially suppose equal dimension of all entries. It determines the need to use short enough 8-byte phrase parts, easy for procession by mass platforms with 8-bit microcontrollers with embedded arithmetic summation and logic XOR operations. The scheme for such shortened LL is proposed further for the documenting of tasks, transmitted by phrases composed of $g$ parts and including check coefficients ${\mathrm{C}}_{1,\mathrm{m}-1}^{\mathrm{K},\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{d}\mathrm{e}\mathrm{r}},{\mathrm{C}}_{2,\mathrm{m}-1}^{\mathrm{K},\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{t}},\dots .,$ ${\mathrm{C}}_{\mathrm{g},\mathrm{m}-1}^{\mathrm{K},\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$. The basic version of LL is citated for comparison in Table 7 (a) with more convenient arrangement of indexes, as in AGA the order of succession is not substantial for input variables. Initially defined model corresponds to the truth table where the newcomer entry is ${\mathbf{e}}_{\mathrm{m}}=\left({\mathrm{e}}_{1,\mathrm{m}},\dots ,{\mathrm{e}}_{\mathrm{n},\mathrm{m}}\right),$ the previous entry is ${\mathbf{e}}_{\mathrm{m}-1}=\left({\mathrm{e}}_{1,\mathrm{m}-1},\dots ,{\mathrm{e}}_{\mathrm{n},\mathrm{m}-1}\right)$, and approving sets of hash values are ${\mathbf{h}}_{\mathrm{m}}=\left({\mathrm{h}}_{1,\mathrm{m}},\dots ,{\mathrm{h}}_{\mathrm{Q},\mathrm{m}}\right)$and ${\mathbf{h}}_{\mathrm{m}-1}=\left({\mathrm{h}}_{1,\mathrm{m}-1},\dots ,{\mathrm{h}}_{\mathrm{Q},\mathrm{m}-1}\right).$Time moments stamps for entries are $t_m$ and $t_{m-1}$.

Then in order to raise the variability of data traffic one can enlarge the number of total check coefficients $C_{i,j}^K$, used in content parts of phrases. Note that coefficients $C_{i,j}^K$ contain randomly assigned hash values besides predictable work parameters. Such version of LL in Table 7 (b) is designated for dialog communications of agents, if intensive replication of instructions or data is undesirable due to unreliable network, weak hardware, financial motives, or commercial and technology secrets. In this case, the mass approving of entries by external network nodes like in blockchain scheme [66,67,68] is problematic, and data approving is to be based on phrase parameters, fixed by the partner agent or by reserve copies in a pair of loyal or trusted agents.

Exp. (8) demonstrates the formal logic notation of truth table given in Table 7 (b).

$$\begin{gathered} h^{\left(out\right)}= \\ {h}^{\left(\mathrm{1,1}\right)}\star X_m\left(\mathrm{1,1}\right)\star X_t\left(t_1,t_1\right)\star X_{C,\mathrm{1,1}}\left(C_{\mathrm{1,1}},C_{\mathrm{1,1}}\right)\star \dots \star X_{C,g,1}\left(C_{g,1},C_{g,1}\right)\star \\ {X}_{h,\mathrm{1,1}}\left(h_{\mathrm{1,1}},h_{\mathrm{1,1}}\right)\star X_{C,\mathrm{1,2}}\left(C_{\mathrm{1,2}},C_{\mathrm{1,2}}\right)\star \dots \star X_{C,g,2}\left(C_{g,2},C_{g,2}\right)\star { X}_{h,\mathrm{1,2}}\left(h_{\mathrm{1,2}},h_{\mathrm{1,2}}\right)+\dots + \\ {h}^{\left(m-\mathrm{1,1}\right)}\star X_m\left(m-1,m-1\right)\star X_t\left(t_{m-1},t_{m-1}\right)\star X_{C,1,m-2}\left(C_{1,m-2},{Ce}_{1,m-2}\right)\star \dots \star \\ {X}_{C,g,m-2}\left(C_{g,m-2},C_{g,m-2}\right)\star X_{h,1,m-2}\left(h_{1,m-2},h_{1,m-2}\right)\star X_{C,1,m-1}\left(C_{1,m-1},C_{1,m-1}\right)\star \\ \dots \star X_{C,g,m-1}\left(C_{g,m-1},C_{g,m-1}\right)\star X_{h,1,m-1}\left(C_{1,m-1},C_{1,m-1}\right)+ h^{(m,1)}\star X_m\left(m,m\right)\star \\ {X}_t\left(t_m,t_m\right)\star X_{C,1,m-1}\left(C_{1,m-1},C_{1,m-1}\right)\star \dots \star X_{C,g,m-1}\left(C_{g,m-1},C_{g,m-1}\right)\star \\ {X}_{h,m,m-1}\left(h_{m,m-1},h_{m,m-1}\right)\star { X}_{C,1,m}\left(C_{1,m},C_{1,m}\right)\star \dots \star X_{C,g,m}\left(C_{g,m},C_{g,m}\right)\star \\ {X}_{h,m,m}\left(h_{m,m},h_{m,m}\right) \end{gathered}$$

(8)

However, for simple robots and IoT with primarily non-confidential data one can further shorten the volume of dialog data and simplify the set of instructions by means of adaptation of ${LL}_{wrd}$, providing direct output of requested group of words.

Adapted AGA function ${LL}_{wrd}^{ad}$can be written by exp. (9)

$$w_{v,m}^K=F_{wrd}(w_{v,m}^N,v,m,h_{v,m}^{\left(m,0\right)},h_{v,m})$$

(9)

which includes the rearranged parameters $w_{v,m}^K$ and$h_{v,m}^{\left(m,0\right)}$and is discussed in sec. 6, Table 10.As in fact $w_{v,m}^K$ are also quasi random hash values taken from one QRNG, then one can quite freely permute them instead of quasi random hash values $h_{v,m}^{\left(m,0\right)}$ earlier assigned by

Addresser. Parole $h_{v,m}$ or Sender`s approving hash is considered as a randomly chosen key for the access to data in another agent, but in more exhausted schemes one can define various paroles for different groups of agents. Microassembler modelling for the function exp.(9) of the simplified LL is presented in sec.6.

One should note that schemes given above doesn`t exclude other variants. As the structure of a phrase was chosen consisting of equal 8-byte parts, one can e.g., use theversion of LL sequentially mixing entries, formed by the header and the 1^st content part, the 1^st content part and the 2d content part, etc.. However, the detailed discussion of it needs to discuss possible tasks and efficiency criteria, what is out of this paper.

Proposed above schemes give the formal logic base for autonomous selective documenting of agent`s parameters in local distributed data storages.

However, verification algorithms should be supplemented by human checks.

5. Results: Fragmentation of AGA Function into Diagrams of Logic States for Verification

The most obvious way to held selective verification procedure is to map the set of critical data from the holistic logic model onto low-dimensional 1D, 2D or 3D charts or diagrams of logic parameters, which are convenient for quick visual checks by human experts, who are the final authority. For verification e.g., in the position-based cryptography and route passing tasks [22], one can use time diagrams of visits to check points, 2D space maps of alternatively visited checkpoints or cargo terminals, time diagrams of the execution of the quantum protocol and verification procedures [52,53]. But the design of such procedures for AGA needs to give several definitions.

Definition 5.

Fragmented mapping function (FMF)$F\left(x_l,\dots ,x_m\right)$ taken within AGA is the result of the injective mapping $F(x_1,\dots ,x_n)\to F(x_l,\dots ,x_m)$, where:

1)$n,l,m N=\left\{\mathrm{0,1},\dots ,k-1\right\}$,$m\ge$l, and $n-1\ge m-l,$(i.e. the mapping shortens the number of initially taken input variables);

2) truth tables of the mapping function$F\left(x_1,\dots ,x_n\right)$and the mapped one$F\left(x_l,\dots ,x_m\right)$have:

a) identical data in columns for coinciding input variables $x_l,\dots ,x_m$;

b) identical logic constants$C_k$in columns for output variables $F\left(x_l,\dots ,x_m\right)$and$F\left(x_1,\dots ,x_n\right)$.

Consequence.FMF can be defined for any sample of initially given input variables. For its practical formation one should simply strike out further in Table 8 all columns for unused input variables, not included into the necessary set ${\mathrm{x}}_{\mathrm{l}},\dots ,{\mathrm{x}}_{\mathrm{m}}$.

Definition 6.

The fragmented map$M$of the fragmented mapping function$F(x_l,\dots ,x_m)$is the group of points, mapping all given samples of input variables$x_l,\dots ,x_m$from the truth table onto the arbitrarily chosen set of: 1) logic constants [$C_{k1},..,C_{k2}]$, where$C_{k1,k2} \left\{1,..,k-1\right\},$or

2) output variables$x_j$, j$\left\{l,..,m\right\}$.

Note. The fragmented map $M$ shows the location of all objects or events with the chosen class given by the constant $C_k$; the limiting band for logic constants or input variables corresponds to critical parameters given by the task.

Definition 7.

Fragmented mapping function (FMF) is named the verification function (VF), if it belongs to the list of formal criteria$L_e$, formed and checked by the knowledge expert.

Given above definitions are illustrated further by Table 8, demonstrating the example of formation of FMF $F(x_3,x_4)$ by striking out unnecessary variables $x_1,x_2,x_5$ from the initially given truth table. We suppose that coordinates $x_3,x_4$ correspond to space ot parameters $x,y,$ which can be the correlated ones, if e.g., the FMF $F\left(x_3,x_4\right)$ shows the location of visited by robot objects or checkpoints. As correlated space and time variables (see sec.2.3) are considered in AGA model as different logic variables, they also can be selected for checks. Principally, any 2D or 3D mapping diagrams like$F\left(x,t\right), F\left(x,y\right),$ or$F(x,y,t)$, given in the band $[0, k-1]$, can be considered as verification functions if adopted by the knowledge expert. 2D logic diagram in fact resembles group point images, known in star navigation systems [81], which can be checked directly on the display or may be additionally processed.

It is necessary to accent the fact, that FMF can be formed arbitrarily for visual checks, but the reverse aggregation into a new AGA functions needs to monitor the values of all the variables, for which FMF was initially defined. The reason is that according to basic definitions of AGA [51], any notation like $F\left(x_i,x_j \right)=F\left(\mathrm{0,0},...,0\right)*X_i\left(a_i,b_i\right){*X}_j\left(a_j,b_j\right)$ always can be extended to the function expression $F\left(x_i,x_j,x_k\right)=F(\mathrm{0,0},...,0)*X_i\left(a_i,b_i\right){*X}_j\left(a_j,b_j\right){*X}_k\left(0,K-1\right)$, where the band from 0 up to $K-1$ will exceed the ranks of earlier used model.

Reverse equivalent representation from truth levels codes $w_{v,m}^{ K}$ back into natural numbers ones $w_{v,m}^{ N}$ can help to receive more visual and convenient groups of parameters, and logic diagrams taken with various limitations are expected to be useful for more complicated data analysis during the debugging of mobile agents. Namely the natural numbers coding of words can help to form convenient groups of data for further planned verification procedures. Figure 11 shows the idea of such logic point group images, obtained for 2D logic diagrams taken from Table 8 with restriction $C_k=\left\{\mathrm{5,6}\right\}$, which correspond to some vocabularies $V_{v,m}^K$. For visual checks by human experts, it can be useful to connect additionally points of the logic diagram by lines. Even the simplest 1D functions $F\left(x_i\right)=F\left(\mathrm{0,0},...,0\right)*X_i\left(a_i,b_i\right),$ $i[\mathrm{0,1},\dots , k-1]$ also corresponds to the given above definition of FMF and may describe numbers of agents and their licenses, obtained parameters, or passed distances.

Given above Defs. (5÷7) describe FMF via truth tables, but basing on AGA template matching and distributed linked list schemes [53,54] one can directly use equivalent representations of the truth table by logic expressions given in sec.2. For AGA logic diagram truth levels always have fixed values and only the number of involved logic constants and their relative location in the diagram may differ. Consequently, AGA-based logic diagrams are the more simple case of check images in contrast to, e.g., contours in stars navigation systems [81].

Thus, FMF scheme enlarges the spectrum of possibilities for human verification and small-scale local memory storages. Due to the fact, that LL is AGA function, it can be used not only as a holistic data structure, but also as a data source for FMF dubbed in a local distributed memory storage. However, all these variants need to discuss hardware requirements. Here the goal is to demonstrate the possibility to realize proposed methods by means of the simplest 8-bit platform, corresponding to IoT level.

6. Results: Communication Module and Microassembler Software for the Verification

The possibility to process the proposed vocabularies structure and the adapted LL scheme is demonstrated by means of the microassembler code and 8-bit circuit board, which was already used in [53,54,59]. Such choice is determined by three factors, and the first of them is to test new AI procedures for IoT devices level, where one don`t use special complicated AI software shells, NN, and specific microprocessors. The second reason is the design of the communication module, which should unload the decision making module in agent. The third reason is that the communication module of agent should protect as much as possible the system from illegal codes and data, what traditionally infers low-level programming based on detailed understanding of memory resources.

Now proposed programs complement a dozen of microassembler subroutines for LL scheme, which were earlier presented in [53,54] and disclosed basic necessary functions of AGA for agent operation and its interface with PC. Given microassembler software was tested in the so-called dual-chip module [53,54,59], based on two 24 MHz ATMEL microcontrollers MCS-51. Nevertheless, the enlarged set of procedures for dialog communications needs to propose the adequate solution for the communications module, which is shown in Figure 12 and is formed by the pair of sequentially connected microcontroller dual-chip cascades from [53,54,59], modified by digital 8-bit feedback bus. It`s role is to provide flexible forward/backward data exchange berweeh modules, controlled by means of several control pins. The bidirectional transfer of data is supposed to be used as between “upper” and “lower” dual-chip modules, as for other peripheral modules. Like in [53,54] the conjugation with the peripheral devices is to use bus registers, triggered on the leading edge.

The advantage of such device is the pair of conjugated microcontrollers connected to common data and address buses, what provides the possibility to use them in parallel or to exploit the doubled set of operators (500-600 ones per MCS-51) for the joint volume of information written in SRAM and ROM. Such structure simplifies the programming of AGAprocedures and helps to separate data acquisition and procession.

Besides this, it gives more possibilities to combine connections of pins and to add new trigger registers for alternative memory chips connected to the common data bus. Two types of integrated memory SRAM and ROM chips are to separate fixed and optional parameters. Such cascaded scheme with microcontrollers currently had 1 MB SRAM and 512 KB EEPROM external memory chips, which were connected to common data buses and provided free enough data resending and memory planning for laboratory experiments. That is the reason to use dual-chip schemes instead of commercial kits like Arduino [82], although they can use greater work frequencies.

For simplicity we don`t discuss here possible radiofrequency and optoelectronic data channels, and the specifics to connect them to the dual- chip scheme. In any way for such designs one needs to describe transmitters/receivers by some vocabularies and to reserve memory resources and free pins in microcontrollers for control signals. These steps can somewhat enlarge the overall time response due to the increased number of control pins and trigger registers, but for the proposed scheme of vocabularies the only requirement is to use equal 8-byte parts of phrases and to coordinate all equivalent vocabularies. As in [54], trigger registers Rg1, 2, and 3 are intended for SRAM addressing, where pins $\overline{CE, }$ $\overline{OE}$, $\overline{WE}$ control read/write process. Banks P0 in MCI and MCII are used for data exchange with SRAM&ROM. Port P3 in MCII is used for clocking procedures, where direct and inverted signals of pins P3.0-P3.4 control read/write procedures. The first of dual-chip schemes is to interact with data receivers/transmitters and is supposed to transmit received data to SRAM into the second dual-chip module. Respectively, the procession of fixed and assigned paroles together with verification procedures was considered for the second one.

In order to use the same EEPROM in dual-chip circuit boards as in [53,54], parameters $v,m$ for vocabularies $V_{v,m}^K$ were taken $v=16$, m=16, the number of root vocabularies $q$ was also taken to be 16, what gives 4096 different words $w_{v,m}^K;$ this responds to multiplexing of 16 root words into 16 subsets and once again multiplexing into 16 next ones. One should especially note, that although every vocabulary contains up to 16 different words, memory allocation tables provides natural number codes and corresponding truth levels codes in the band {1÷255}, where zero means the not used parameter. For advanced systems, Addresser may “demand” additional credentials and ask additional questions to Sender for the full access to the vocabularies structure.However, for simple robots in IoT one can shorten the number of dialog phrases and simplify the set of instructions by means of the adaptation of ${LL}_{wrd}$, providing direct output of requested group of words. As various specialized agents may be allowed to use only selected groups of vocabularies, they should keep in memory the preliminary given table of access paroles or fixed hashes ${\mathrm{h}}_{\mathrm{v},\mathrm{m}}$ and approval hashes ${\mathrm{h}}^{(\mathrm{m},0)}$, which principally may be chosen different for various groups of robots.

In the present paper the main task of modeling was to show the possibility to use the proposed vocabulary structure and adapted LL scheme for the verification of confidential enough data, where one avoids direct full data transfer, and Sender of phrase only checks the correctness of actual for him words by means of correct template hidden in ${LL}_{wrd}$. Variant of memory allocation table for the adapted version of the linked list ${LL}_{wrd}$ is shown in Table 10; it resembles schemes used in [54], but here both SRAM and EEPROM chips were used. This adapted AGA function ${LL}_{wrd}$follows exp.(10) $w_{v,m}^K=F_{wrd}(w_{v,m}^N,v,m,h_{v,m}^{\left(m,0\right)},h_{v,m})$ taken with rearranged parameters $w_{v,m}^K$ and$h_{v,m}^{\left(m,0\right)}$. Due to the fact, that $w_{v,m}^K$ are also quasi random hash values, one can rearrange it with another quasi random hash values $h_{v,m}^{\left(m,0\right)}$ assigned by Addresser, what corresponds to definitions of LL [53,54].

Table 10. Memory allocation table used for modelling of ${LL}_{wrd}$. .

N	Word code in natural numbers,${\mathbf{w}}_{\mathbf{v},\mathbf{m}}^{\mathbf{N}}$={1÷16}	$\mathbf{Number}\mathbf{of}\mathbf{row}\mathbf{in}\mathbf{vocabulary}\mathbf{matrix},$$\mathbf{v}=\left\{116\right\}$	Number of column in vocabulary matrix, m={1÷16}	Addresser approving$\mathbf{hash},$${\mathbf{h}}_{\mathit{v},\mathit{m},}^{(\mathit{m},0)}$={1÷256}	$\mathbf{Sender}\mathbf{approving}\mathbf{hash},$${\mathbf{h}}_{\mathbf{v},\mathbf{m}}=1256\}$	Word code in truth levels, ${\mathbf{w}}_{\mathbf{v},\mathbf{m}}^{\mathbf{K}}=${1÷256}
#A18 –A16:	#000b	#000b	#000b	#000b	#000b	#000b
#SB (A15-A8):	#109	#108	#107	#106	#105	#104
#LB:	#0÷255	#0÷255	#0÷255	#0÷255	#0÷255	#0÷255

Table 10. Memory allocation table used for modelling of ${LL}_{wrd}$. .

N	Word code in natural numbers,${\mathbf{w}}_{\mathbf{v},\mathbf{m}}^{\mathbf{N}}$={1÷16}	$\mathbf{Number}\mathbf{of}\mathbf{row}\mathbf{in}\mathbf{vocabulary}\mathbf{matrix},$$\mathbf{v}=\left\{116\right\}$	Number of column in vocabulary matrix, m={1÷16}	Addresser approving$\mathbf{hash},$${\mathbf{h}}_{\mathit{v},\mathit{m},}^{(\mathit{m},0)}$={1÷256}	$\mathbf{Sender}\mathbf{approving}\mathbf{hash},$${\mathbf{h}}_{\mathbf{v},\mathbf{m}}=1256\}$	Word code in truth levels, ${\mathbf{w}}_{\mathbf{v},\mathbf{m}}^{\mathbf{K}}=${1÷256}
#A18 –A16:	#000b	#000b	#000b	#000b	#000b	#000b
#SB (A15-A8):	#109	#108	#107	#106	#105	#104
#LB:	#0÷255	#0÷255	#0÷255	#0÷255	#0÷255	#0÷255

Further modelling is demonstrated by the microassembler subroutine LLWRD shown in Algorithm 3. It refers to the the adapted version of the linked list ${LL}_{wrd}$ proposed above in sec. 4 and described in Table 10. It`s role is to approve correctness of the truth levels code for some of words $w_{v,m}^K$, according to the request sent by an external agent Sender, which should declare several passwords to Addresser and to check the correctness of his version of truth levels code for actual coded words, using template data written in ${LL}_{wrd}$ in Addresser.

The second presented program fragment of the subroutine CHKPHR is shown in Algorithm 4 and refers to the formal procession of the header part of the phrase by Addresser, as the consideration of content part needs to analyze the vast structure of typical agent`s tasks.

Both procedures are supposed to be carried out in the communication module of agent, which is to carry out preliminary procession of messages, as the full scale AI modeling is the prerogative of the decision-making module.

Microassembler subroutine LLWRD is given in Algorithm 3 and continues earlier designed set of software programs presented in for the dual–chip scheme and the base version of LL. It partially intersects with basic algorithms given as Tables 12-13-14 in [54], but there only SRAM was involved. Here EEPROM was used as the data storage for template (or correct) data, and SRAM was to keep data to be checked, which were received from Sender. EEPROM chip needs separate addressing to compute a set of non-zero product terms ${\{pt}_1,$…, ${pt}_m\}$ [53,54].The same #SB addresses (## 107÷103) were reserved for the ${LL}_{wrd}$ in SRAM and EEPROM to shorten the re-switching of pins. Also, instead of calculation of the operator MIN in pairs ${PT}_m=MIN(h^{\left(m,1\right)},{pt}_m$) [54], more short program LLWRD directly assigns logic constant $h^{\left(m,1\right)}$ to the non-zero product term ${pt}_m$ with the result saved in #SB=#103. Algorithm 3 demonstrates simple adaptation of vocabularies structure to the LL scheme. If necessary, some more complicated versions can be used for dialog polling and data approving.

Algorithm 3. Subroutine LLWRD is to compute correct truth levels codes for the requested elements of vocabulary $V_{v,m}^K$ and $V_{v,m}^N$. Procedure is to be carried out in MCS-III of 2d dual-chip and uses its pins.
	INPUT: $w_{v,m,}^N,{\mathrm{v},m,h}_{v,m},h_{v,m}^{(m,0)}$ $\leftarrow$Input variables
1	LLWRD: CLR P1.4; prepare pin	2	MOV P2,#000b; Assign #A18-A16=#000b for SRAM
3	CLR P1.7; enable Rg1 by $\overline{CE}$	4	SETB P1.4; Rg1 writes #A15-A8=#000b
5	CLR P1.4;	6	SETB P1.7 ; lock Rg1
7	CYCNT: MOV R2,#255; Set counter of notations	8	CYCVAR: MOV R3,#5; counter of input vars
9	LOAT:MOV P2,#009b; set #SB at to Rg3/7 ROM	10	CLR P1.5; enable Rg3/7 by $\overline{CE}$
11	SETB P1.4; Rg3/7 writes #SB=#009b for a-template	12	CLR P1.4;
13	SETB P1.5; lock Rg3/7	14	MOV P2,R2; set #A7-A0=#255 for at ROM
15	CLR P1.2; enable ROM$by\overline{ CE}$	16	CLR P3.1; enable ROM output $by\overline{ OE}$
17	REAT:MOV R7,P0; read$at$from ROM	18	SETB P3.1; disable ROM output $by\overline{ CE}$
19	LOBT: MOV P2,#109; load #SB of bt in ROM	20	CLR P1.6; enable Rg3/7 by $\overline{CE}$
21	SETB P1.4; Rg3/7 writes #SB=#109 of b-template	22	CLR P1.4;
23	SETB P1.6; lock Rg3/7	24	MOV P2,#255; set #LB=#255 for ROM
25	CLR P1.2; enable chip ROM$by\overline{ CE}$	26	CLR P3.1; $\overline{ OE}$enables ROM output
27	REBT:MOV R6,P0; read$b$-template from ROM	28	SETB P3.1; disable ROM output
29	SETB P1.2; disable chip ROM	30	CLR P1.1; prepare pin for SRAM
31	LOAE: MOV P2,#0; set #SB=0 in Rg1/5for SRAM	32	CLR P1.6; $\overline{CE}$enables Rg2
33	SETB P1.4; write #SB=#0 to Rg2	34	CLR P1.4
35	SETB P1.6; lock Rg2	36	MOV P2,R3 ; #LB counter of variables
37	CLR P1.3; $\overline{CE}$enables SRAM	38	CLR P1.1;$\overline{OE}$enables output of SRAM
39	REAE:MOV R5,P0; read $a$-external from SRAM	40	SETB P1.1; disable output of SRAM
41	SETB P1.3; disable SRAM	42	LITERAL: MOV A,R7; load a-template to calc Lit.
43	CLR C; prepare carry bit	44	SUBB A, R5; at-ae=R7-R5
45	JC CAB; jump if carry bit C=1,i.e. a-ext. >a-templ.	46	AJMP PT0;Lit=0 and the whole pt=0
47	CAB: CLR C	48	MOV A,R6; load bt to A to calc Literal
49	CLR C; prepare carry bit	50	SUBB A,R5; bt-ae=R6-R5
51	JC PT0; jump PT0 if bit C=1, i.e. ae> bt	52	DEC R3; counter of input vriables
53	CJNE R3,#0,LOAT; process next variable	54	PT1: AJMP WRRES; write const in #SB=#003
55	PT0: MOV R0, #0; product term=#0	56	AJMP WRR0
57	WRRES: MOV P2,#4 ; set #SB=#004 to read Const	58	SETB P1.4; write #SB=#004 into Rg2/6
59	CLR P1.6; enable Rg2/6	60	CLR P1.4;
61	MOV P2,R3 ; assign #LB to read Const	62	CLR P1.3; $\overline{CE}$enables chip SRAM
63	CLR P1.1; $\overline{OE}$enables output of SRAM	64	RECNST:MOV R0,P0; write Const in R0
65	SETB P1.1; disable output of SRAM	66	SETB P1.6; disable Rg2/6
67	WRR0: MOV P2,#3; set #SB=#003 to write Const	68	CLR P1.6; enable RG2/6
69	SETB P1.4; write #SB=#003 to Rg2	70	CLR P1.4;
71	SETB P1.6; lock Rg2 with #003	72	MOV P2,R2; addressing of #LB for SRAM
73	MOV P0,R0; output next Const	74	CLR P1.3; $\overline{CE}$enables chip SRAM
75	CLR P1.1; $\overline{OE}$enables data of SRAM	76	CLR P1.0; write Const in #SB=003, #LB=R2
77	SETB P1.0;$\overline{WE}$disables write in SRAM	78	SETB P1.1; $\overline{OE}$disables data of SRAM
79	SETB P1.3; $\overline{OE}$disables chip SRAM	80	DJNZ R2,#1,CYCVAR; process next notation
81	MAXPTS:MOV R1,#103; #SB103 for PTs	82	MOV R2,#255; counter of PTs
83	MOV P2,R1; addressing #SB=#103	84	CLR P1.6; enable Rg2by$\overline{CE}$
85	SETB P1.4; write #SB=#103 to Rg2	86	CLR P1.4
87	SETB P1.6; lock Rg2	88	MOV P2,R2 ; #LB is the counter of PTs
89	CLR P1.3; enable SRAM by$\overline{CE}$	90	CLR P1.1;$\overline{OE}$enables output of SRAM
91	MOV A,P0; read PT	92	SETB P1.1; disable output of SRAM
93	SETB P1.3; disable SRAM	94	DEC R2
95	NEXTPT:MOV P2,R2	96	CLR P1.3; enable SRAM by$\overline{CE}$
97	CLR P1.1;$\overline{OE}$enables output of SRAM	98	MOV R7,P0; read next PT
99	SETB P1.1; disable output of SRAM	100	SETB P1.3; disable SRAM
101	MOV R3,A; save value of Acc	102	CLR C
103	SUBB A,R7;	104	JNC MAX_N1
105	MOV R0,R7	106	MAX_N1:MOV R0,R3
107	DJNZ R2, NEXTPT	108	RETI
	OUTPUT: R0 →$w_{v,m}^K$, truth levels code for the requested word from $V_{v,m}^K$is written into the register R0

The fragment of the second microassembler program CHKPHR is to find correct parts in the buffer and for brevity is given fragmented. Input data buffer in SRAM of the 2d dual-chip uses the allocation memory table given in Table 11. Memory reserve fields are necessary to write intermediate calculations and results.

Further Algorithm 4 demonstrates the initial fragment of the microassembler program CHKPHR to process the initiation word, to check input parole, to check addresser, to calculate total check coefficient summation, and to compare it with the declared value, i.e. it can determine correct header in the buffer.

Algorithm 4. The fragment of subroutine CHKPHR is to detect header part of phrase and to calculate its total check coefficient in the buffer data. Register R7 is the counter for 30 parts in the buffer segment, R6 is the counter of parts in the phrase, R5 - counter of #LB, R4 - counter of word values (limited by 16).
$\mathbf{I}\mathbf{n}\mathbf{p}\mathbf{u}\mathbf{t}:$		${\mathit{W}}_{\mathit{h}}=\left\{w_{\mathrm{1,1}}^K,w_{\mathrm{1,2}}^K{, w}_{\mathrm{1,4}}^K,w_{\mathrm{2,4}}^K,w_{\mathrm{3,4}}^K,w_{\mathrm{1,5}}^K,w_{\mathrm{2,5}}^K,w_{\mathrm{3,5}}^K\right\}$					$\leftarrow$Header of the received phrase parts
		${\mathit{W}}_{\mathit{c}}^{\mathit{*}}=\left\{w_{\mathrm{1,1}}^K,w_{\mathrm{1,2}}^K{, w}_{\mathrm{1,4}}^K,w_{\mathrm{2,4}}^K,w_{\mathrm{3,4}}^K,w_{\mathrm{1,5}}^K,w_{\mathrm{2,5}}^K,w_{\mathrm{3,5}}^K\right\}$					$\leftarrow$Error 8-byte part
		${\mathit{W}}_{\mathit{c}}=\left\{w_{\mathrm{1,3}}^K,w_{\mathrm{1,8}}^K,w_{\mathrm{2,8}}^K,w_{33,s}^K,w_{\mathrm{1,4}}^K,w_{\mathrm{2,4}}^K,w_{\mathrm{3,4}}^K, C_{total}^{N/K}\right\}$					$\leftarrow$Correct content part of phrase
		$w_{\mathrm{1,2}}^K=7=Hi, read 2 parts,$					$\leftarrow$Words interpretation in the decoding table
		${ w}_{\mathrm{1,2}}^K=123=Hi, read 3 parts,$
		$w_{\mathrm{1,2}}^K=209=Hi, read 4 parts$
1	FINDHI: CLR P1.4; prepare pin				2	MOV P2,#00000111b; Assign #A18-A16=#000b
3	CLR P1.7; enable Rg1 by $\overline{CE}$				4	SETB P1.4; Rg1 writes #A15-A8=#111b
5	CLR P1.4				6	SETB P1.7 ; lock Rg1
7	CYCPT: MOV R7,#1; counter of 30 parts in buffer				8	MOV P2,#00000111b; Assign #SB=#1 to read header
9	CLR P1.6; enable Rg2 by $\overline{CE}$				10	SETB P1.4; Rg1 writes #SB=A15-A8=#1
11	CLR P1.4;				12	SETB P1.6 ; lock Rg2
13	NXTPRT1:MOV R5,#0; counter of #LB				14	NXTPRT11:MOV P2,R5; set #LB
15	REWRD1: CLR P1.3; enable chip SRAM by $\overline{CE}$				16	CLR P1.1; enable data output from SRAM
17	CHKHI1:MOV R3,P0; read 1st word from SRAM				18	MOV R0,R3; copy # of 1st word for further summation
19	SETB P1.1; disable output of SRAM				20	SETB P1.3; disable chip of SRAM
21	CHKHI11: CJNE R3, #7, CHKHI2; check if $w_{\mathrm{1,1}}^K$=7				22	MOV R6,#2; determines number of parts in phrase g=2
23	AJMP CHKPWD;				24	CHKHI2: CJNE R3, #123, CHKHI3; check if $w_{\mathrm{1,1}}^K$=123
25	MOV R6,#3; number of parts in phrase g=3				26	AJMP CHKPWD;
27	CHKHI3: CJNE R3, #209, NXTPRT2; check if =#209				28	MOV R6,#4; number of parts in phrase g=4
29	CHKPWD: INC R5; #LB of 2d word - parole				30	MOV P2, R5; # to read password
31	CLR P1.3; enable chip SRAM by $\overline{CE}$				32	CLR P1.1; enable data output from SRAM by $\overline{OE}$
33	PWD:MOV R3,P0; output 2d word from SRAM				34	SETB P1.1; disable output of SRAM
35	SETB P1.3; disable chip of SRAM				36	CJNE R3,#131,NXTPRT2; password =131
37	AJMP CHKNAME1;				38	NXTPRT2: DEC R5; return to the 1st word
39	NXTPRT21:MOV A,R5;				40	ADD A,#7; #LB for the 1st word in next part
41	MOV R5,A; #LB				42	MOV R1,A; copy #LB of word for further calc
43	CJNE R5,#240,NXTPRT11; check if buffer passed				44	RETI; buffer is fully processed
45	CHKNAME1: INC R5; #LB+1				46	INC R5; #LB increased by 2 for Addresser name 1
47	MOV P2,R5; #LB to read name1				48	NOP;
49	CLR P1.3; enable chip SRAM by$\overline{CE}$				50	CLR P1.1; enable data output from SRAM
51	RENAME1:MOV R3,P0; read name1				52	SETB P1.1; disable data output from SRAM
53	SETB P1.3; disable chip of SRAM				54	CJNE R3, #0, DEC2LB; name1 is =#0
55	INC R1; #LB for Addresser name2				56	CHKNAME2: MOV P2,R1; read name2
57	CLR P1.3; enable chip SRAM by$\overline{CE}$				58	CLR P1.1; enable data output from SRAM
59	RENAME2:MOV R3,P0; read name2				60	SETB P1.1; disable data output from SRAM
61	SETB P1.3; disable chip of SRAM				62	CJNE R3, #0, DEC2LB; name2 is =#0
63	INC R0; #LB for Addresser name 3				64	CHKNAME3: MOV P2,R3; read name3
65	CLR P1.3; enable chip SRAM by$\overline{CE}$				66	CLR P1.1; enable data output from SRAM
67	RENAME3: MOV R3,P0; read next $word$				68	SETB P1.1; disable data output from SRAM
69	SETB P1.3; disable chip of SRAM				70	CJNE R3, #3, DEC2LB; name 3 =#3
71	AJMP CHKHSUM1				72	DEC2LB: DEC R5;
73	DEC R5;				74	DEC R5; return #LB to 1st word in phrase
75	AJMP NXTPRT21				76	CHKHSUM1:MOV R1,#0; counter of words
77	DEC R5;				78	DEC R5;
79	DEC R5; return #LB to 1st word in phrase				80	HSUM1: MOV R0, R5; copy #LB of word
81	MOV P2,R5; #LB 1st word of header				82	MOV A,#0; clear A for summation
83	CLR P1.3; enable chip SRAM by $\overline{CE}$				84	CLR P1.1; enable data output from SRAM
85	MOV R3,P0; read $word$ from SRAM				86	MOV R1,#0; counter of words in phrase
87	SETB P1.1; disable output of SRAM				88	SETB P1.3; disable chip of SRAM
89	HSUM2: ADD A,R3;				90	INC R1; counter of words in part
91	INCR5:INC R5; increment #LB +1				92	CJNE R1,#8,HSUM1; check counter of words
93	WRHSUM: MOV R4,A; save header check sum				94	CJNE R5,#240,RETI
95	WRCNTPT: MOV R1,#240; write check coef. to Reserve 1				96	ADD R5,#8; # LB for next part
97	CJNE R5,#240,RETI				98	RECNTWD: P2,R5; #LB to read 1st content word
99	CLR P1.3; $\overline{CE}$enables chip SRAM				100	CLR P1.1; $\overline{OE}$enables output of SRAM
101	CLR P1.0				102	MOV P0,R3; read sender name3
103	SETB P1.0; disable write				104	SETB P1.1; disable chip SRAM
105	SETB P1.3				…	…
…		RETI			…	…
Output:		buffer Reserve1→		R4 contains total check coefficient for the adequate header ${\mathit{W}}_{\mathit{h}}=\left\{w_{\mathrm{1,1}}^K,w_{\mathrm{1,2}}^K{, w}_{\mathrm{1,4}}^K,w_{\mathrm{2,4}}^K,w_{\mathrm{3,4}}^K,w_{\mathrm{1,5}}^K,w_{\mathrm{2,5}}^K,w_{\mathrm{3,5}}^K\right\}$and is ready to use it further

Carried out microassembler modeling, algorithms, and subroutines complement earlier done designs of AGA operators MINIMUM, MAXIMUM, LITERAL, and C language version of AGA function calculation, published earlier in open access papers [52,53,54]. For brief approximate comparison of time characteristics one can use reference basic data given in [53], where operators need t _MIN-MAX

4 µs and t _Literal

9 µs; the calculation of AGA function with $K=256$ truth levels and $n=12$variables takes$\mathrm{210,000}$work cycles and 0,1 s at 24 MHz. Such time response is comparable with human time response in dialog mode. The computing time for other subroutines can be approximately estimated by the comparison of the number of used operators in various programs.

Results of modelling.

• The proposed structure of coded vocabularies and the conjugated dialog protocol are tested by two microassembler programs, designed for the dual–chip module based on 8-bit microcontrollers MCS-51. They demonstrate principal compatibility of proposed tools with devices of IoT level, provide close complexity level and can be combined together with earlier published algorithms [53,54,59] for the calculations of AGA functions and the base LL scheme.
• The designed dialog phrase protocol for agents communication, involving 8-bytes header and content parts, is compatible and convenient enough for the procession by 8-bit dual-chip module.
• Designed vocabularies structure can be used in simple 8-bit platforms with limited free memory resources, and the proposed dialog protocol can selectively transfer various combinations of logic words and verification coefficients.
• AGA vocabularies structure in 8-bit modelling provides 256 coded words$w_{v,m}^K$ and $w_{v,m}^N$, what gives the possibility to form complicated enough terminology chains and to design tasks descriptions for distant exchange of data.
• Adapted version of LL with 5 input variables is the minimalistic possible tool for protected local storages of critical data, protected by paroles and hash values. If necessary, intermediate versions of LL can be extended by means of the enlarged number of hash values, approving the LL by other internal and external modules.
• Proposed subroutine LLWRD is compatible with algorithms published earlier in [52,53] and complements AGA subroutines for XOR calculations in [53]. Also one can use the software from for connection to PC.
• Designed algorithms are applicable both for truth levels codes $w_{v,m}^K$ and natural numbers ones $w_{v,m}^N$, what can be further used for new and more exhausted verification schemes in the heterogeneous logic architecture of agent.

Further research needs to design universal algorithm and microassembler subroutine of template AGA function, which can be flexibly adapted for the procession of all proposed versions of LL scheme, i.e. can be re-switched by the choice of appropriate control parameters. That will help to avoid excessive software in dual-chip module, which is limited by 500-600 operators per one MCS-51. SRAM microscheme in dual-chip module potentially can be enlarged up to 32 MB.

Vocabularies structure and words codes should be further applied to the dual-chip scheme itself and to commercial robotic platforms like Arduino, in order to imitate peripheral AI procedures in decision making module and to involve standard wireless network modules.

7. Discussion

Further research of the proposed vocabularies structure and dialog mode of verification refers to the design of control models for large scale robotic systems, where only administrators and supervising agents possess holistic formal logic model, and separate groups of robots has only fragmentary knowledge and sets of subroutines. In such a system, full-scale modelling in every agent is too expensive and excessive, and the reasonable strategy is to reconfigure the individual agent model for the current task and situation. Then autonomous schemes of missing knowledge search, exchange and verification of reconfigured models become the key element. Another aspect of the problem is to adapt the structure of vocabularies and WM to specialized fragments, appropriate for the design of transformable and self-learning robots with changeable tools. The expected complication here is that verification procedures should be enlarged to monitor the compatibility of robotic hardware platforms, accessible tools, and corresponding software.

Close actual task is the extension of the proposed vocabularies structure to the control of the WM, describing the operation of agent in the scene of action and activating corresponding subroutines and actuators. This goal follows from the review of robotic WMs [62], where the main contribution was to design explicit dimensions of WMs, to determine the underlying principles to make decisions, and to search the trade-offs model for conflict situations. The conclusion of the authors of was that the universal WM does not exist, as it highly depends on the robotic system, the environment in which it operates, and the performed tasks. Even simple robot can use more than one WM, e.g., one for navigation and another one for manipulation. Respectively, the procession of complicated vocabularies structure for ${\mathit{V}}_{\mathit{v},\mathit{m}}^{\mathit{L},\mathit{N},\mathit{K}}$ is the realistic scheme for WM modeling and can be extended to the selection of activated expressions and software subroutines. However, the choice of vocabularies and words may itself include special calculations and estimations based on expert knowledge. Then WM can be considered as the comprehensive current structure of vocabularies subsets, whose choice is to be done by the decision-maker for the specific current task, basing on rules of work, objects detected in the scene of action, current goals, instructions received from the owner of robots, and behavior of people and robots in the scene. Such research also seems to include complicated AI optimization and AGA metrics, estimating the distance to the formal aim in the multi-parametric space.

Proposed FMF remains here a service tool, which good correlates with the idea of distributed small-scale local memory storages used in the network MAS. The motivated structure of hidden and protected by LL data storages for irregular checks can be preliminary prepared and activated by microcontrollers without special high-level robotic languages. The proposed dialog protocol provides access to data basing on content control, and real addresses for such data storages will be hidden for external agents. Minimalistic versions of LL storages with enough number of passwords should be complemented by confidential digital map of addresses for specific vocabularies sets.

The proposed simple adaptation of basic LL scheme for small scale robotic collective creates the task to select several most actual template versions of LL for enhanced AI modelling, including content analysis and parametrical passwords, adaptable to various external conditions. In small-scale groupes of agents the adaptive structure of LLs is to be attributed to the history of the completed work, can complement one-time quasi random passwords in verification procedures.

As the microcontroller-based communications module and its re-coding tables for $w_{v,m}^{ K}$ and $w_{v,m}^{ N}$ are divorced from the decision-making module and mass Internet tools for data procession, then one receives the opportunity to cut off incorrect external codes from AGA contours. The development of allocated communication module with extended verification procedures gives the potential possibility to control and to exclude the illegal loading of external codes into the decision-making subsystem of agent via the interface with PC and the network card. Then the design of AGA-controlled verification scheme is to be extended from the communication module also to the interface between the decision-maker and standard USB module with wireless network hardware.

One more actual problem is the slow enough progress in robotic computer vision [13,14] and the real success in fake images generation [83], what limits the development of verification methods. In such extensively developing fields as IoV and the positioning of delivery drones, advanced verification procedure should integrate not only space and time parameters of routes, but also to use formal monitoring of images of cargo, terminals, territorial restrictions, and the biometrics of personnel. Further research is to disclose, how useful can be the conjugation of AGA models and NN. At least it is to compensate the known problem of deliberate data correction in NN [22].

In a small-scale MAS without distinctly pronounced statistical characteristics of agents behaviour, the application of quantum computing for verification seems not to be a priority task. However, this situation can be changed greatly for the global robotic system or for the imitation of human creative algorithms, where it will be necessary to generate and compare many alternative AGA expressions. Then simple in essence AGA vocabularies structure logic modelling and verification algorithms can help to unite quantum procedures and collective robotic tasks.

8. Conclusions

Technical faults, attacks and illegal data modification make distant data verification the obligatory component of collective robotic systems. Verification is considered as the set of data integrity and authentication tests, activated for initial debugging of the agent, periodical testing, work correction, and system restoration. Verification procedures can be initiated not only by a distant administrator or partner robots from the same MAS, but also by state regulator`s agents and loyal or conflicting external robots. Verification tasks motivate to use non-exhausted selective check procedures and distributed local data storages for critical data documenting, protected by LL schemes. Verification should combine automatic and human checks.

In the presented paper robotic communications and verification procedures are firstly proposed to be based on AGA logic model, using ordered high capacity vocabularies structure and formal logic dialog language. AGA-based robotic language and dialog phrases protocol are defined by the ordered matrix structure of vocabularies $V_{v,m}^N$ and $V_{v,m}^K$ formed by logic words $w_{v,m}$. Firstly, the scene of actions, robots, objects, tasks, tools, and involved software products are to be described by the preliminary formed structure of natural language words and their collocations, represented by vocabularies $V^L$given in the natural language. Further vocabularies$V^L$ are to be mapped onto the ones $V^N$, represented by natural numbers codes, which in its turn should be mapped onto vocabularies $V^K$ formed by truth levels codes defined in AGA. Such three-levels structure of equivalent coding provides the optional use of not protected natural numbers codes and of quasi-random truth levels codes, preventing from illegal data modification, and providing enhanced data integrity checks and the search of errors.

Phrases in dialogs of robots are to be coded by truth levels codes and transmitted by parts, formed by 8-byte sequences of coded numbers. Proposed protocol provides the possibility to find correct content parts of the phrase, what gives the principal possibility to transfer them in parallel even with time delays, e.g., by different laser wavelengths or various radio frequencies in wireless data lines. The procession of the phrase is proposed to be done by AGA-based functions, realizing high capacity finite automatons for the verification of phrases. AGA template matching or logic filtering of input logic phrases is to be used further for the formal preliminary interpretation of phrases. Such procession procedures don`t disclose real physical values of coded internal parameters of agent.

In order to provide reliable documenting of data in the distributed set of local data storages in network agents, the presented paper proposes adapted versions of AGA-based LL. The firstly proposed scheme of mapping of multi-parametric logic AGA functions onto truth levels scale provides small dimensional (1D, 2D, 3D) fragmented projections (or logic diagrams) convenient both for human and automatic checks, as well as for critical data saving in local storages in network agents. Such diagrams can help to visualize and to find errors in verified data.

Wide bands of time, space and some other parameters can be obtained by means of correlated input logic variables taken in AGA, what provides the chance to extend the proposed communications protocol for large-scale systems.

Algorithms and software modelling are demonstrated for the allocated 8-bit microcontroller module, included into the dual-chip microcontroller scheme, earlier used for MVL-LL design. The cascaded scheme of two dual-chip nodules is considered as a platform for communication module for further verification and AI modelling.

Designed MVL-schemes are based on the heterogeneous logic architecture of agent, what gives the methodology to combine AGA, traditional Boolean and fuzzy logic.