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Factorization of Boolean Polynomials: Parallel Algorithms and Experimental Evaluation

Emelyanov, PG and Krishna, M and Kulkarni, V and Nandy, SK and Ponomaryov, DK and Raha, S (2021) Factorization of Boolean Polynomials: Parallel Algorithms and Experimental Evaluation. In: Programming and Computer Software, 47 (2). pp. 108-118.

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Official URL: https://doi.org/10.1134/S0361768821020043


Abstract: Polynomial factorization is a classical algorithmic algebra problem with a wide range of applications. Of particular interest is factorization over finite fields, among which fields of order two are probably the most important ones when representing Boolean functions by Zhegalkin polynomials. In particular, factorization of Boolean polynomials corresponds to conjunctive decomposition of Boolean functions given in algebraic normal form. In addition, factorization enables decomposition of functions given in full disjunctive normal form (DNF) and positive DNF, as well as Cartesian decomposition of relational data. These applications demonstrate the importance of developing fast factorization algorithms. In this paper, we consider some recently proposed factorization algorithms of polynomial complexity and describe a parallel MIMD implementation that takes advantage of both task-level and data-level parallelism. We conduct some experiments on logic synthesis benchmarks and synthetic (random) polynomials to demonstrate significant factorization speedup. In conclusion, we discuss results of testing a parallel implementation of the algorithm on a massively parallel multicore architecture (REDEFINE). © 2021, Pleiades Publishing, Ltd.

Item Type: Journal Article
Publication: Programming and Computer Software
Publisher: Pleiades journals
Additional Information: The copyright for this article belongs to Pleiades journals
Keywords: Boolean functions; Computational complexity; Logic Synthesis; Polynomials; Software architecture, Data-level parallelism; Decomposition of functions; Disjunctive normal form; Experimental evaluation; Factorization algorithms; Multicore architectures; Parallel implementations; Polynomial factorization, Factorization
Department/Centre: Division of Interdisciplinary Sciences > Computational and Data Sciences
Date Deposited: 10 Aug 2021 10:43
Last Modified: 10 Aug 2021 10:43
URI: http://eprints.iisc.ac.in/id/eprint/69115

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