Fast Decision Procedures Based on Congruence Closure
Journal of the ACM (JACM)
Deciding Combinations of Theories
Journal of the ACM (JACM)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
A DPLL-Based Calculus for Ground Satisfiability Modulo Theories
JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
A Generalization of Shostak's Method for Combining Decision Procedures
FroCoS '02 Proceedings of the 4th International Workshop on Frontiers of Combining Systems
A Rewrite Rule Based Framework for Combining Decision Procedures
FroCoS '02 Proceedings of the 4th International Workshop on Frontiers of Combining Systems
RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
FME '02 Proceedings of the International Symposium of Formal Methods Europe on Formal Methods - Getting IT Right
CVC: A Cooperating Validity Checker
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Checking Satisfiability of First-Order Formulas by Incremental Translation to SAT
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Commutation, Transformation, and Termination
Proceedings of the 8th International Conference on Automated Deduction
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Integrating decision procedures for temporal verification
Integrating decision procedures for temporal verification
Decision procedures in automated deduction
Decision procedures in automated deduction
Journal of Automated Reasoning
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Architecting Solvers for SAT Modulo Theories: Nelson-Oppen with DPLL
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
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Implementing efficient algorithms for combining decision procedures has been a challenge and their correctness precarious. In this paper we describe an inference system that has the classical Nelson-Oppen procedure at its core and includes several optimizations: variable abstraction with sharing, canonization of terms at the theory level, and Shostak's streamlined generation of new equalities for theories with solvers. The transitions of our system are fine-grained enough to model most of the mechanisms currently used in designing combination procedures. In particular, with a simple language of regular expressions we are able to describe several combination algorithms as strategies for our inference system, from the basic Nelson-Oppen to the very highly optimized one recently given by Shankar and Rueß. Presenting the basic system at a high level of generality and nondeterminism allows transparent correctness proofs that can be extended in a modular fashion when new features are introduced in the system.