Combining matching algorithms: The regular case
Journal of Symbolic Computation
Combining unification algorithms
Journal of Symbolic Computation
Normalized rewriting: an alternative to rewriting modulo a set of equations
Journal of Symbolic Computation
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
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)
The Cassowary linear arithmetic constraint solving algorithm
ACM Transactions on Computer-Human Interaction (TOCHI)
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
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
Journal of Automated Reasoning
Simplify: a theorem prover for program checking
Journal of the ACM (JACM)
Efficient theory combination via boolean search
Information and Computation - Special issue: Combining logical systems
Decision procedures for extensions of the theory of arrays
Annals of Mathematics and Artificial Intelligence
A comprehensive combination framework
ACM Transactions on Computational Logic (TOCL)
New results on rewrite-based satisfiability procedures
ACM Transactions on Computational Logic (TOCL)
Electronic Notes in Theoretical Computer Science (ENTCS)
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Automatic combinability of rewriting-based satisfiability procedures
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Nelson-Oppen, shostak and the extended canonizer: a family picture with a newborn
ICTAC'04 Proceedings of the First 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
What's decidable about arrays?
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
Proof-producing congruence closure
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
The algebra of equality proofs
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
On superposition-based satisfiability procedures and their combination
ICTAC'05 Proceedings of the Second international conference on Theoretical Aspects of Computing
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
A calculus for generating ground explanations
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
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Decision procedures are key components of theorem provers and constraint satisfaction systems. Their modular combination is of prime interest for building efficient systems, but their effective use is often limited by poor interface capabilities, when such procedures only provide a simple ''sat/unsat'' answer. In this paper, we develop a framework to design cooperation schemas between such procedures while maintaining modularity of their interfaces. First, we use the framework to specify and prove the correctness of classic combination schemas by Nelson-Oppen and Shostak. Second, we introduce the concept of deduction complete satisfiability procedures, we show how to build them for large classes of theories, then we provide a schema to modularly combine them. Third, we consider the problem of modularly constructing explanations for combinations by re-using available proof-producing procedures for the component theories.