Abstract
We present an extension of the BC tableau, a calculus for determining satisfiability of constrained Boolean circuits. We argue that a satisfiability decision procedure based on the BC tableau can be implemented as a non-clausal DPLL procedure and that therefore, advances to the DPLL framework can be integrated into such a tableau procedure. We present a prototypical implementation of these ideas and evaluate it using a set of benchmark instances. We show that the extensions increase the efficiency of the basic BC tableau considerably and compare the performance of our solver with that of the non-clausal solver NoClause and the CNF-based SAT solver MiniSat.
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Notes
The improvement concerns the space requirement in the worst case: the original procedure requires exponential space, whereas, for the improved procedure, the space requirement is polynomial in the size of the input formula.
From a practical point of view, it is sufficient to consider only the original variables in the solving process. From a proof-theoretical point of view, considering additional variables can be beneficial [18].
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Egly, U., Haller, L. A SAT Solver for Circuits Based on the Tableau Method. Künstl Intell 24, 15–23 (2010). https://doi.org/10.1007/s13218-010-0008-4
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DOI: https://doi.org/10.1007/s13218-010-0008-4