Parallel Factorization of Boolean Polynomials

Vadiraj Kulkarni, Pavel Emelyanov, Denis Ponomaryov, Madhava Krishna, Soumyendu Raha, S. K. Nandy

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

Abstract

Polynomial factorization is a classical algorithmic problem in algebra, which has a wide range of applications. Of special interest is factorization over finite fields, among which the field of order two is probably the most important one due to the relationship to Boolean functions. In particular, factorization of Boolean polynomials corresponds to decomposition of Boolean functions given in the Algebraic Normal Form. It has been also shown that factorization provides a solution to decomposition of functions given in the full DNF (i.e., by a truth table), for positive DNFs, and for cartesian decomposition of relational datatables. These applications show the importance of developing fast and practical factorization algorithms. In the paper, we consider some recently proposed polynomial time factorization algorithms for Boolean polynomials and describe a parallel MIMD implementation thereof, which exploits both the task and data level parallelism. We report on an experimental evaluation, which has been conducted on logic circuit synthesis benchmarks and synthetic polynomials, and show that our implementation significantly improves the efficiency of factorization. Finally, we report on the performance benefits obtained from a parallel algorithm when executed on a massively parallel many core architecture (Redefine).

Original languageEnglish
Title of host publicationPerspectives of System Informatics - 12th International Andrei P. Ershov Informatics Conference, PSI 2019, Revised Selected Papers
EditorsNikolaj Bjørner, Irina Virbitskaite, Andrei Voronkov
PublisherSpringer International Publishing AG
Pages80-94
Number of pages15
ISBN (Print)9783030374860
DOIs
Publication statusE-pub ahead of print - 16 Dec 2019
Event12th International Andrei P. Ershov Informatics Conference, PSI 2019 - Novosibirsk, Russian Federation
Duration: 2 Jul 20195 Jul 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11964 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference12th International Andrei P. Ershov Informatics Conference, PSI 2019
CountryRussian Federation
CityNovosibirsk
Period02.07.201905.07.2019

Keywords

  • Boolean polynomials
  • Factorization
  • Reconfigurable computing

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