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- W2258308757 abstract "We propose an approach for decomposing Boolean satisfiability problems while extending recent results of cite{sul2} on solving Boolean systems of equations. Developments in cite{sul2} were aimed at the expansion of functions $f$ in orthonormal (ON) sets of base functions as a generalization of the Boole-Shannon expansion and the derivation of the consistency condition for the equation $f=0$ in terms of the expansion co-efficients. In this paper, we further extend the Boole-Shannon expansion over an arbitrary set of base functions and derive the consistency condition for $f=1$. The generalization of the Boole-Shannon formula presented in this paper is in terms of emph{cofactors} as co-efficients with respect to a set of CNFs called a emph{base} which appear in a given Boolean CNF formula itself. This approach results in a novel parallel algorithm for decomposition of a CNF formula and computation of all satisfying assignments when they exist by using the given data set of CNFs itself as the base." @default.
- W2258308757 created "2016-06-24" @default.
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- W2258308757 date "2014-12-07" @default.
- W2258308757 modified "2023-09-27" @default.
- W2258308757 title "Generalized cofactors and decomposition of Boolean satisfiability problems." @default.
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