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Algebraic Polynomial Sum Solver Over $\{0, 1\}$
Version 1
: Received: 1 August 2019 / Approved: 5 August 2019 / Online: 5 August 2019 (03:31:23 CEST)
Version 2 : Received: 26 November 2019 / Approved: 29 November 2019 / Online: 29 November 2019 (07:28:14 CET)
Version 3 : Received: 4 April 2020 / Approved: 6 April 2020 / Online: 6 April 2020 (12:57:55 CEST)
Version 4 : Received: 15 April 2020 / Approved: 16 April 2020 / Online: 16 April 2020 (10:17:03 CEST)
Version 5 : Received: 18 September 2020 / Approved: 19 September 2020 / Online: 19 September 2020 (09:51:02 CEST)
Version 6 : Received: 10 February 2021 / Approved: 11 February 2021 / Online: 11 February 2021 (11:56:37 CET)
Version 2 : Received: 26 November 2019 / Approved: 29 November 2019 / Online: 29 November 2019 (07:28:14 CET)
Version 3 : Received: 4 April 2020 / Approved: 6 April 2020 / Online: 6 April 2020 (12:57:55 CEST)
Version 4 : Received: 15 April 2020 / Approved: 16 April 2020 / Online: 16 April 2020 (10:17:03 CEST)
Version 5 : Received: 18 September 2020 / Approved: 19 September 2020 / Online: 19 September 2020 (09:51:02 CEST)
Version 6 : Received: 10 February 2021 / Approved: 11 February 2021 / Online: 11 February 2021 (11:56:37 CET)
How to cite: Vega, F. Algebraic Polynomial Sum Solver Over $\{0, 1\}$. Preprints 2019, 2019080037 (doi: 10.20944/preprints201908.0037.v6). Vega, F. Algebraic Polynomial Sum Solver Over $\{0, 1\}$. Preprints 2019, 2019080037 (doi: 10.20944/preprints201908.0037.v6).
Abstract
Given a polynomial $P(x_{1}, x_{2}, \ldots, x_{n})$ which is the sum of terms, where each term is a product of two distinct variables, then the problem $APSS$ consists in calculating the total sum value of $\sum_{\forall U_{i}} P(u_{1}, u_{2}, \ldots, u_{n})$, for all the possible assignments $U_{i} = \{u_{1}, u_{2}, ... u_{n}\}$ to the variables such that $u_{j} \in \{0, 1\}$. $APSS$ is the abbreviation for the problem name Algebraic Polynomial Sum Solver Over $\{0, 1\}$. We show that $APSS$ is in $\#L$ and therefore, it is in $FP$ as well. The functional polynomial time solution was implemented with Scala in \url{https://github.com/frankvegadelgado/sat} using the DIMACS format for the formulas in $\textit{MONOTONE-2SAT}$.
Subject Areas
complexity classes; polynomial time; reduction; logarithmic space
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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