Deciding Combinations of Theories
Journal of the ACM (JACM)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
A Generalization of Shostak's Method for Combining Decision Procedures
FroCoS '02 Proceedings of the 4th International Workshop on Frontiers of Combining Systems
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
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
A rewriting approach to satisfiability procedures
Information and Computation - RTA 2001
A Decision Procedure for an Extensional Theory of Arrays
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
AI Communications - CASC
Modular proof systems for partial functions with Evans equality
Information and Computation - Special issue: Combining logical systems
Rewrite-Based Satisfiability Procedures for Recursive Data Structures
Electronic Notes in Theoretical Computer Science (ENTCS)
Rewrite-Based Decision Procedures
Electronic Notes in Theoretical Computer Science (ENTCS)
Decision procedures for extensions of the theory of arrays
Annals of Mathematics and Artificial Intelligence
Efficient E-Matching for SMT Solvers
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
${\mathcal{T}}$-Decision by Decomposition
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Automatic Decidability and Combinability Revisited
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Hierarchical and Modular Reasoning in Complex Theories: The Case of Local Theory Extensions
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
Noetherianity and Combination Problems
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
New results on rewrite-based satisfiability procedures
ACM Transactions on Computational Logic (TOCL)
Building extended canonizers by graph-based deduction
ICTAC'07 Proceedings of the 4th international conference on Theoretical aspects of computing
Automatic decidability and combinability
Information and Computation
On Deciding Satisfiability by Theorem Proving with Speculative Inferences
Journal of Automated Reasoning
JELIA'06 Proceedings of the 10th European conference on Logics in Artificial Intelligence
Automatic combinability of rewriting-based satisfiability procedures
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Decision procedures for the formal analysis of software
ICTAC'06 Proceedings of the Third international conference on Theoretical Aspects of Computing
Decidability and undecidability results for nelson-oppen and rewrite-based decision procedures
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
On superposition-based satisfiability procedures and their combination
ICTAC'05 Proceedings of the Second international conference on Theoretical Aspects of Computing
Bounded model checking of software using SMT solvers instead of SAT solvers
SPIN'06 Proceedings of the 13th international conference on Model Checking Software
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The rewriting approach to $\mathcal{T}$-satisfiability is based on establishing termination of a rewrite-based inference system for first-order logic on the $\mathcal{T}$-satisfiability problem. Extending previous such results, including the quantifier-free theory of equality and the theory of arrays with or without extensionality, we prove termination for the theories of records with or without extensionality, integer offsets and integer offsets modulo. A general theorem for termination on combinations of theories, that covers any combination of the theories above, is given next. For empirical evaluation, the rewrite-based theorem prover E is compared with the validity checkers CVC and CVC Lite, on both synthetic and real-world benchmarks, including both valid and invalid instances. Parametric synthetic benchmarks test scalability, while real-world benchmarks test ability to handle huge sets of literals. Contrary to the folklore that a general-purpose prover cannot compete with specialized reasoners, the experiments are overall favorable to the theorem prover, showing that the rewriting approach is both elegant and practical.