Algebraic Polynomial Sum Solver Over $\{0, 1\}$

Frank Vega

doi:10.20944/preprints201908.0037.v6

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preprints.org > computer science and mathematics > computer science > doi: 10.20944/preprints201908.0037.v6

Preprint Article Version 6 Preserved in Portico This version is not peer-reviewed

Algebraic Polynomial Sum Solver Over $\{0, 1\}$

Frank Vega

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 7 : Received: 19 August 2021 / Approved: 27 August 2021 / Online: 27 August 2021 (14:09:47 CEST)
Version 8 : Received: 20 October 2021 / Approved: 26 October 2021 / Online: 26 October 2021 (11:07:59 CEST)
Version 9 : Received: 7 March 2024 / Approved: 8 March 2024 / Online: 8 March 2024 (11:06:11 CET)
Version 10 : Received: 14 March 2024 / Approved: 14 March 2024 / Online: 14 March 2024 (10:11:13 CET)
Version 11 : Received: 14 March 2024 / Approved: 15 March 2024 / Online: 18 March 2024 (08:29:48 CET)
Version 12 : Received: 29 March 2024 / Approved: 1 April 2024 / Online: 1 April 2024 (17:14:22 CEST)
Version 13 : Received: 6 April 2024 / Approved: 6 April 2024 / Online: 8 April 2024 (06:04:04 CEST)
Version 14 : Received: 11 April 2024 / Approved: 11 April 2024 / Online: 12 April 2024 (04:51:11 CEST)

How to cite: Vega, F. Algebraic Polynomial Sum Solver Over $\{0, 1\}$. Preprints 2019, 2019080037. https://doi.org/10.20944/preprints201908.0037.v6 Vega, F. Algebraic Polynomial Sum Solver Over $\{0, 1\}$. Preprints 2019, 2019080037. https://doi.org/10.20944/preprints201908.0037.v6

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MDPI and ACS Style

Vega, F. Algebraic Polynomial Sum Solver Over $\{0, 1\}$. Preprints 2019, 2019080037. https://doi.org/10.20944/preprints201908.0037.v6

APA Style

Vega, F. (2021). Algebraic Polynomial Sum Solver Over $\{0, 1\}$. Preprints. https://doi.org/10.20944/preprints201908.0037.v6

Chicago/Turabian Style

Vega, F. 2021 "Algebraic Polynomial Sum Solver Over $\{0, 1\}$" Preprints. https://doi.org/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 $\textit{MONOTONE-2SAT}$.

Keywords

complexity classes; polynomial time; reduction; logarithmic space

Subject

Computer Science and Mathematics, Computer Science

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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Comments (1)

Comment 1

Received: 11 February 2021
Commenter: Frank Vega
Commenter's Conflict of Interests: Author

Comment: The new version was implemented and tested and therefore, this is a validated paper with new arguments. The title, keyword, abstract and content were changed.

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