Substitutional Definition of Satisfiability in Classical Propositional Logic

Belov, Anton; Stachniak, Zbigniew

doi:10.1007/11499107_3

Cited by 1 publication

(1 citation statement)

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“…Our generalisation of a SAT solver's solution is based on the efficient computation of a minimal solution of a given conjunctive normal form (CNF) formula. Our approach is thus similar in spirit to the so-called MinSat problem and its variations [6,8,15], which, however, are known to be NPcomplete [8]. These complexity theoretic results imply that we cannot hope to find any generally efficient algorithm and therefore, we need to resort to heuristic approaches which (as our benchmarks in this paper indicate) work well in most practically relevant cases.…”

Section: Existing Approaches To Smtmentioning

confidence: 94%

Don’t care in SMT: building flexible yet efficient abstraction/refinement solvers

Bauer

Leucker

Schallhart

et al. 2009

Int J Softw Tools Technol Transfer

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This paper describes a method for combining "off-the-shelf" SAT and constraint solvers for building an efficient Satisfiability Modulo Theories (SMT) solver for a wide range of theories. Our method follows the abstraction/refinement approach to simplify the implementation of custom SMT solvers. The expected performance penalty by not using an interweaved combination of SAT and theory solvers is reduced by generalising a Boolean solution of an SMT problem first via assigning don't care to as many variables as possible. We then use the generalised solution to determine a thereby smaller constraint set to be handed over to the constraint solver for a background theory. We show that for many benchmarks and real-world problems, this optimisation results in considerably smaller and less complex constraint problems. The presented approach is particularly useful for assembling a practically viable SMT solver quickly, when neither a suitable SMT solver nor a corresponding incremental theory solver is available. We have implemented our approach in the ABsolver framework and applied the resulting solver successfully to an industrial case-study: the Supported by the DFG research grant FORTAS (VE 455/1-1).

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