On Efficiently Integrating Boolean and Theory-Specific Solving Procedures

Efficient decision procedures have been conceived in different communities for a very heterogeneous collection of expressive decidable theories. However, despite in the last years we have witnessed an impressive advance in the efficiency of SAT procedures, techniques for efficiently integrating boolean reasoning and theory-specific decision procedures have been deeply investigated only recently, producing impressive performance improvements when applied. The goal of this paper is to analyze, classify and represent within a uniform framework the most effective techniques which have been proposed in various communities in order to maximize the efficiency of boolean reasoning within decision procedures. 1 Motivation and goals In the last decade we have witnessed an impressive advance in the efficiency of SAT techniques, which has brought large previously intractable problems at the reach of state-of-the-art solvers [38, 12, 46]. As a consequence, some hard real-world problems have been successfully solved by encoding them into SAT. Propositional planning [28] and boolean model-checking [13] are among the best achievements. Unfortunately, simple boolean expressions are not expressive enough for representing many real-world problems. Efficient decision procedures for expressive decidable theories have been conceived in different communities, like, e.g., automated theorem proving, knowledge representation and reasoning, AI planning, formal verification. These procedures involve a very heterogeneous collection of theories, like modal logics [23, 42, 25, 21], description logics [24, 26, 32, 25], difference logic [1, 4, 29, 2], linear arithmetic [44, 4], logic of equality and uninterpreted functions (EUF) [18, 8, 20], logics of bit arrays and inductive datatypes [18, 8, 41], and, more generally, decidable subclasses of first order logic [8, 10, 43, 11]. In these communities a big effort has been concentrated in producing ad hoc procedures of increasing expressiveness and efficiency, and in combining them in the most efficient way [31, Sponsored by the CALCULEMUS! IHP-RTN EC project, code HPRN-CT-2000-00102, by a MIUR COFIN02 project, code 2002097822 003, and by a grant from the Intel Corporation.