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

Projective cofactor decompositions of Boolean functions and the satisfiability problem