Handbook of theoretical computer science (vol. B)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
A rewriting approach to satisfiability procedures
Information and Computation - RTA 2001
New results on rewrite-based satisfiability procedures
ACM Transactions on Computational Logic (TOCL)
Splitting without backtracking
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Decidability and undecidability results for nelson-oppen and rewrite-based decision procedures
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
On superposition-based satisfiability procedures and their combination
ICTAC'05 Proceedings of the Second international conference on Theoretical Aspects of Computing
Automatic Decidability and Combinability Revisited
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Combining Proof-Producing Decision Procedures
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
Theory decision by decomposition
Journal of Symbolic Computation
Combination of convex theories: Modularity, deduction completeness, and explanation
Journal of Symbolic Computation
Automatic decidability and combinability
Information and Computation
Modular termination and combinability for superposition modulo counter arithmetic
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
An Instantiation Scheme for Satisfiability Modulo Theories
Journal of Automated Reasoning
Rewriting Computation and Proof
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We address the problems of combining satisfiability procedures and consider two combination scenarios: (i) the combination within the class of rewriting-based satisfiability procedures and (ii) the Nelson-Oppen combination of rewriting-based satisfiability procedures and arbitrary satisfiability procedures. In each scenario, we use meta-saturation, which schematizes saturation of the set containing the axioms of a given theory and an arbitrary set of ground literals, to syntactically decide sufficient conditions for the combinability of rewriting-based satisfiability procedures. For (i), we give a sufficient condition for the modular termination of meta-saturation. When meta-saturation for the union of theories halts, it yields a rewriting-based satisfiability procedure for the union. For (ii), we use meta-saturation to prove the stable infiniteness of the component theories and deduction completeness of their rewriting-based satisfiability procedures. These properties are important to establish the correctness of the Nelson-Oppen combination method and to obtain an efficient implementation.