Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
A rewriting approach to satisfiability procedures
Information and Computation - RTA 2001
Model-Theoretic Methods in Combined Constraint Satisfiability
Journal of Automated Reasoning
A comprehensive combination framework
ACM Transactions on Computational Logic (TOCL)
On Variable-inactivity and Polynomial T-Satisfiability Procedures
Journal of Logic and Computation
LFCS '07 Proceedings of the international symposium on Logical Foundations of Computer Science
New results on rewrite-based satisfiability procedures
ACM Transactions on Computational Logic (TOCL)
On Deciding Satisfiability by DPLL($\Gamma+{\mathcal T}$) and Unsound Theorem Proving
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Combinable Extensions of Abelian Groups
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Locality Results for Certain Extensions of Theories with Bridging Functions
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Theory decision by decomposition
Journal of Symbolic Computation
Decision procedures for algebraic data types with abstractions
Proceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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
Combining Satisfiability Procedures for Unions of Theories with a Shared Counting Operator
Fundamenta Informaticae - On the Italian Conference on Computational Logic: CILC 2009
Automatic combinability of rewriting-based satisfiability procedures
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
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Modularity is a highly desirable property in the development of satisfiability procedures. In this paper we are interested in using a dedicated superposition calculus to develop satisfiability procedures for (unions of) theories sharing counter arithmetic. In the first place, we are concerned with the termination of this calculus for theories representing data structures and their extensions. To this purpose, we prove a modularity result for termination which allows us to use our superposition calculus as a satisfiability procedure for combinations of data structures. In addition, we present a general combinability result that permits us to use our satisfiability procedures into a non-disjoint combination method à la Nelson-Oppen without loss of completeness. This latter result is useful whenever data structures are combined with theories for which superposition is not applicable, like theories of arithmetic.