A canonical form for generalized linear constraints
Journal of Symbolic Computation
On Fourier's algorithm for linear arithmetic constraints
Journal of Automated Reasoning
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
Model-Theoretic Methods in Combined Constraint Satisfiability
Journal of Automated Reasoning
A theoretical basis for the reduction of polynomials to canonical forms
ACM SIGSAM Bulletin
A comprehensive combination framework
ACM Transactions on Computational Logic (TOCL)
On Variable-inactivity and Polynomial T-Satisfiability Procedures
Journal of Logic and Computation
New results on rewrite-based satisfiability procedures
ACM Transactions on Computational Logic (TOCL)
On superposition-based satisfiability procedures and their combination
ICTAC'05 Proceedings of the Second international conference on Theoretical Aspects of Computing
On theorem proving for program checking: historical perspective and recent developments
Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming
On Deciding Satisfiability by Theorem Proving with Speculative Inferences
Journal of Automated Reasoning
Modular termination and combinability for superposition modulo counter arithmetic
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
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We apply an extension of the Nelson-Oppen combination method to develop a decision procedure for the non-disjoint union of theories modeling data structures with a counting operator and fragments of arithmetic. We present some data structures and some fragments of arithmetic for which the combination method is complete and effective. To achieve effectiveness, the combination method relies on particular procedures to compute sets that are representative of all the consequences over the shared theory. We show how to compute these sets by using a superposition calculus for the theories of the considered data structures and various solving and reduction techniques for the fragments of arithmetic we are interested in, including Gauss elimination, Fourier-Motzkin elimination and Groebner bases computation.