${\mathcal{T}}$-Decision by Decomposition

  • Authors:

  • Maria Paola Bonacina;Mnacho Echenim

  • Affiliations:

  • Dipartimento di Informatica, Università degli Studi di Verona, Strada Le Grazie 15, I-39134 Verona, Italy;Dipartimento di Informatica, Università degli Studi di Verona, Strada Le Grazie 15, I-39134 Verona, Italy

  • Venue:
  • CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
  • Year:
  • 2007

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Abstract

Much research concerning Satisfiability Modulo Theories is devoted to the design of efficient SMT-solvers that integrate a SAT-solver with ${\mathcal{T}}$-satisfiability procedures. The rewrite-based approach to ${\mathcal{T}}$-satisfiability procedures is appealing, because it is general, uniform and it makes combination of theories simple. However, SAT-solvers are unparalleled in handling the large Boolean part of ${\mathcal{T}}$-decision problems of practical interest. In this paper we present a decomposition framework that combines a rewrite-based theorem prover and an SMT solver in an off-line mode, in such a way that the prover "compiles the theory away," so to speak. Thus, we generalize the rewrite-based approach from ${\mathcal{T}}$ -satisfiability to ${\mathcal{T}}$-decision procedures, making it possible to use the rewrite-based prover for theory reasoning and the SAT-solver in the SMT-solver for Boolean reasoning. We prove the practicality of this framework by giving decision procedures for the theories of records, integer offsets and arrays.