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A SAT Solver for Circuits Based on the Tableau Method

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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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Algorithm 1
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Notes

  1. 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.

  2. 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].

  3. http://www.kr.tuwien.ac.at/research/systems/BattleAx/.

  4. http://www.tcs.hut.fi/~tjunttil/bcsat.

  5. http://www.cs.toronto.edu/~fbacchus/sat.html.

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Authors and Affiliations

  1. Institute of Information Systems 184/3, KBS Group, TU Wien, Favoritenstraße 9-11, 1040, Wien, Österreich

    Uwe Egly

  2. Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford, OX13QD, UK

    Leopold Haller

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  1. Uwe Egly
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  2. Leopold Haller
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Correspondence to Uwe Egly.

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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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