Cooperation of Decision Procedures for the Satisfiability Problem
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Constraint programming is strongly based on the use of solvers which are able to check satisfiability of constraints. We show in this paper a rule-based algorithm for solving in a modular way the satisfiability problem w.r.t. a class of theories Th. The case where Th is the union of two disjoint theories Th 1 and Th 2 is known for a long time but we study here different cases where function symbols are shared by Th 1 and Th 2. The chosen approach leads to a highly non-deterministic decomposition algorithm but drastically simplifies the understanding of the combination problem. The obtained decomposition algorithm is illustrated by the combination of non-disjoint equational theories.
KeywordsFunction Symbol Constraint Programming Equational Theory Decomposition Algorithm Decision Algorithm
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