Satisfiability Modulo Theories and Assignments

Abstract : The CDCL procedure for SAT is the archetype of conflict-driven procedures for satisfiability of quantifier-free problems in a single theory. In this paper we lift CDCL to CDSAT (Conflict-Driven Satisfia-bility), a system for conflict-driven reasoning in combinations of disjoint theories. CDSAT combines theory modules that interact through a global trail representing a candidate model by Boolean and first-order assignments. CDSAT generalizes to generic theory combinations the model-constructing satisfiability calculus (MCSAT) introduced by de Moura and Jovanovi´cJovanovi´c. Furthermore, CDSAT generalizes the equality sharing (Nelson-Oppen) approach to theory combination, by allowing theories to share equality information both explicitly through equalities and dis-equalities, and implicitly through assignments. We identify sufficient conditions for the soundness, completeness, and termination of CDSAT.
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Maria Bonacina, Stéphane Graham-Lengrand, Natarajan Shankar. Satisfiability Modulo Theories and Assignments. CADE 2017 - 26th International Conference on Automated Deduction, Aug 2017, Gothenburg, Sweden. ⟨10.1007/978-3-319-63046-5_4⟩. ⟨hal-01615830⟩

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