Splitting on demand in SAT Modulo theories

Clark Barrett, Robert Nieuwenhuis, Albert Oliveras, Cesare Tinelli

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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. The delegation 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. This results in drastically simpler theory solvers. We present this idea 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.

Original languageEnglish (US)
Title of host publicationLogic for Programming, Artificial Intelligence, and Reasoning - 13th International Conference, LPAR 2006, Proceedings
PublisherSpringer Verlag
Number of pages15
ISBN (Print)3540482814, 9783540482819
StatePublished - 2006
Event13th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR 2006 - Phnom Penh, Cambodia
Duration: Nov 13 2006Nov 17 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4246 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other13th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR 2006
CityPhnom Penh

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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