Handbook of theoretical computer science (vol. B)
Variations on the Common Subexpression Problem
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)
Unions of non-disjoint theories and combinations of satisfiability procedures
Theoretical Computer Science
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
Shostak's Congruence Closure as Completion
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
ICS: Integrated Canonizer and Solver
CAV '01 Proceedings of the 13th 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
A rewriting approach to satisfiability procedures
Information and Computation - RTA 2001
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
Journal of Automated Reasoning
Strategies for combining decision procedures
TACAS'03 Proceedings of the 9th international conference on Tools and algorithms for the construction and analysis of systems
Distributing the Workload in a Lazy Theorem-Prover
Electronic Notes in Theoretical Computer Science (ENTCS)
CC(X): Semantic Combination of Congruence Closure with Solvable Theories
Electronic Notes in Theoretical Computer Science (ENTCS)
Combining Proof-Producing Decision Procedures
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)
Combination of convex theories: Modularity, deduction completeness, and explanation
Journal of Symbolic Computation
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
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
Efficient satisfiability modulo theories via delayed theory combination
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
On superposition-based satisfiability procedures and their combination
ICTAC'05 Proceedings of the Second international conference on Theoretical Aspects of Computing
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We consider the problem of building satisfiability procedures for unions of disjoint theories. We briefly review the combination schemas proposed by Nelson-Oppen, Shostak, and others. Three inference systems are directly derived from the properties satisfied by the theories being combined and known results from the literature are obtained in a uniform and abstract way. This rational reconstruction is the starting point for further investigations. We introduce the concept of extended canonizer and derive a modularity result for a new class of theories (larger than Shostak and smaller than Nelson-Oppen theories) which is closed under disjoint union. This is in contrast with the lack of modularity of Shostak theories. We also explain how to implement extended canonizers by using the basic building blocks used in Shostak schema or by means of rewriting techniques.