Formal Verification for Fault-Tolerant Architectures: Prolegomena to the Design of PVS
IEEE Transactions on Software Engineering
Term rewriting and all that
Deciding Combinations of Theories
Journal of the ACM (JACM)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
Unions of non-disjoint theories and combinations of satisfiability procedures
Theoretical Computer Science
Validity Checking for Combinations of Theories with Equality
FMCAD '96 Proceedings of the First International Conference on Formal Methods in Computer-Aided Design
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
STeP: Deductive-Algorithmic Verification of Reactive and Real-Time Systems
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
On Shostak's Decision Procedure for Combinations of Theories
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: 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
Strategies for combining decision procedures
TACAS'03 Proceedings of the 9th international conference on Tools and algorithms for the construction and analysis of systems
CC(X): Semantic Combination of Congruence Closure with Solvable Theories
Electronic Notes in Theoretical Computer Science (ENTCS)
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If there exist efficient procedures (canonizers) for reducing terms of two first-order theories to canonical form, can one use them to construct such a procedure for terms of the disjoint union of the two theories? We prove this is possible whenever the original theories are convex. As an application, we prove that algorithms for solving equations in the two theories (solvers) can not be combined in a similar fashion. These results are relevant to the widely used Shostak's method for combining decision procedures for theories. They provide the first rigorous answers to the questions about the possibility of directly combining canonizers and solvers.