Projective cofactor decompositions of Boolean functions and the satisfiability problem

Madhav Desai; Virendra Sule

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arXiv · 1603.04569

Projective cofactor decompositions of Boolean functions and the satisfiability problem

Madhav Desai·Virendra Sule

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Abstract

Given a CNF formula $F$, we present a new algorithm for deciding the satisfiability (SAT) of $F$ and computing all solutions of assignments. The algorithm is based on the concept of \emph{cofactors} known in the literature. This paper is a fallout of the previous work by authors on Boolean satisfiability \cite{sul1, sul2,sude}, however the algorithm is essentially independent of the orthogonal expansion concept over which previous papers were based. The algorithm selects a single concrete cofactor recursively by projecting the search space to the set which satisfies a CNF in the formula. This cofactor is called \emph{projective cofactor}. The advantage of such a computation is that it recursively decomposes the satisfiability problem into independent sub-problems at every selection of a projective cofactor. This leads to a parallel algorithm for deciding satisfiability and computing all solutions of a satisfiable formula.

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Madhav Desai, Virendra Sule. 2016-03-15. Projective cofactor decompositions of Boolean functions and the satisfiability problem. https://arxiv.org/abs/1603.04569

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