Handbook of theoretical computer science (vol. B)
Deciding Combinations of Theories
Journal of the ACM (JACM)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
A rewriting approach to satisfiability procedures
Information and Computation - RTA 2001
AI Communications - CASC
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
Combining data structures with nonstably infinite theories using many-sorted logic
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
FroCoS'05 Proceedings of the 5th international conference 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)
Satisfiability Procedures for Combination of Theories Sharing Integer Offsets
TACAS '09 Proceedings of the 15th International Conference on Tools and Algorithms for the Construction and Analysis of Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009,
Combination of convex theories: Modularity, deduction completeness, and explanation
Journal of Symbolic Computation
Data structures with arithmetic constraints: a non-disjoint combination
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
Automatic decidability and combinability
Information and Computation
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
Superposition for bounded domains
Automated Reasoning and Mathematics
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We study how to efficiently combine satisfiability procedures built by using a superposition calculus with satisfiability procedures for theories, for which the superposition calculus may not apply (e.g., for various decidable fragments of Arithmetic). Our starting point is the Nelson-Oppen combination method, where satisfiability procedures cooperate by exchanging entailed (disjunction of) equalities between variables. We show that the superposition calculus deduces sufficiently many such equalities for convex theories (e.g., the theory of equality and the theory of lists) and disjunction of equalities for non-convex theories (e.g., the theory of arrays) to guarantee the completeness of the combination method. Experimental results on proof obligations extracted from the certification of auto-generated aerospace software confirm the efficiency of the approach. Finally, we show how to make satisfiability procedures built by superposition both incremental and resettable by using a hierarchic variant of the Nelson-Oppen method.