Reasoning About Recursively Defined Data Structures
Journal of the ACM (JACM)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
A rewriting approach to satisfiability procedures
Information and Computation - RTA 2001
A Decision Procedure for an Extensional Theory of Arrays
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Decidability of invariant validation for paramaterized systems
TACAS'03 Proceedings of the 9th international conference on Tools and algorithms for the construction and analysis of systems
Combinations of theories for decidable fragments of first-order logic
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
Combining theories: the Ackerman and guarded fragments
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
Combining decision procedures by (model-)equality propagation
Science of Computer Programming
Combination of disjoint theories: beyond decidability
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
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A crucial step in the assertional verification of concurrent programs is deciding whether some sets of literals are satisfiable or not. In this context, the Nelson-Oppen combination scheme is often used. This scheme combines decision procedures for two disjoint theories into a decision procedure for the union of these theories. However, the standard version of the Nelson-Oppen technique tackles only one-sorted, stably infinite first-order theories. The scheme has previously been adapted to a many-sorted framework [C. Tinelli and C. G. Zarba. Combining decision procedures for theories in sorted logics. Technical Report 04-01, Department of Computer Science, The University of Iowa, Feb. 2004], and to handle non-stably infinite theories [C. Tinelli and C. G. Zarba. Combining non-stably infinite theories, in: I. Dahn and L. Vigneron, editors, Proceedings of the 4th International Workshop on First Order Theorem Proving, FTP'03 (Valencia, Spain), Electronic Notes in Theoretical Computer Science 86.1 (2003), Elsevier Science Publishers]. Those two enhancements were presented independently. We propose a unifying version in the continuity of both previous ones, which further relaxes the stably infinite requirement. Notably, some non-stably infinite theories can now be combined with the theory of arrays. Also, the combination scheme is presented here using a semantic notion of theory, allowing to handle non-first order theories.