Preprint Article Version 2 This version is not peer-reviewed

The Entropy Function for Non Polynomial Problems and Its Applications for Turing Machines

Version 1 : Received: 28 January 2020 / Approved: 30 January 2020 / Online: 30 January 2020 (10:53:55 CET)
Version 2 : Received: 28 February 2020 / Approved: 2 March 2020 / Online: 2 March 2020 (15:26:03 CET)
Version 3 : Received: 4 March 2020 / Approved: 5 March 2020 / Online: 5 March 2020 (15:06:23 CET)

How to cite: Santana Lima, M. The Entropy Function for Non Polynomial Problems and Its Applications for Turing Machines. Preprints 2020, 2020010360 (doi: 10.20944/preprints202001.0360.v2). Santana Lima, M. The Entropy Function for Non Polynomial Problems and Its Applications for Turing Machines. Preprints 2020, 2020010360 (doi: 10.20944/preprints202001.0360.v2).

Abstract

We present a general process for the halting problem, valid regardless of the time and space computational complexity of the decision problem. It can be interpreted as the maximization of entropy for the utility function of a given Shannon-Kolmogorov-Bernoulli process. Applications to non-polynomials problems are given. The new interpretation of information rate proposed in this work is a method that models the solution space boundaries of any decision problem (and non polynomial problems in general) as a communication channel by means of Information Theory. We described a sort method that order objects using the intrinsic information content distribution for the elements of a constrained solution space - modeled as messages transmitted through any communication systems. The limits of the search space are defined by the Kolmogorov-Chaitin complexity of the sequences encoded as Shannon-Bernoulli strings. We conclude with a discussion about the implications for general decision problems in Turing machines.

Subject Areas

Computational Complexity; Information Theory; Machine Learning; Computational Statistics; Kolmogorov-Chaitin Complexity; Kelly criterion

Comments (1)

Comment 1
Received: 2 March 2020
Commenter: Matheus Santana Lima
Commenter's Conflict of Interests: Author
Comment: Adding background information and previous work for the TSP.
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