Splitting on Demand in SAT Modulo Theories

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Splitting on Demand in SAT Modulo Theories (2006)

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by Clark Barrett , Robert Nieuwenhuis , Albert Oliveras , Cesare Tinelli

Venue:	In Proc. LPAR’06, volume 4246 of LNAI
Citations:	44 - 14 self

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@INPROCEEDINGS{Barrett06splittingon,
    author = {Clark Barrett and Robert Nieuwenhuis and Albert Oliveras and Cesare Tinelli},
    title = {Splitting on Demand in SAT Modulo Theories},
    booktitle = {In Proc. LPAR’06, volume 4246 of LNAI},
    year = {2006},
    publisher = {Springer}
}

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Abstract

Abstract. Lazy algorithms for Satisfiability Modulo Theories (SMT) combine a generic DPLL-based SAT engine with a theory solver for the given theory T that can decide the T-consistency of conjunctions of ground literals. For many theories of interest, theory solvers need to reason by performing internal case splits. Here we argue that it is more convenient to delegate these case splits to the DPLL engine instead. This can be done on demand for solvers that can encode their internal case splits into one or more clauses, possibly including new constants and literals. It results in drastically simpler theory solvers, and can lead, we believe, to more efficient overall systems. We present this in an improved version of DPLL(T), a general SMT architecture for the lazy approach, and formalize and prove it correct in an extension of Abstract DPLL Modulo Theories, a framework for modeling and reasoning about lazy algorithms for SMT. A remarkable additional feature of the architecture, also discussed in the paper, is that it naturally includes an efficient Nelson-Oppen-like combination of multiple theories and their solvers. 1

Keyphrases

sat modulo theory theory solver lazy algorithm improved version general smt architecture new constant many theory ground literal remarkable additional feature internal case efficient nelson-oppen-like combination satisfiability modulo theory lazy approach multiple theory dpll engine generic dpll-based sat engine abstract dpll modulo theory efficient overall system internal case split

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