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# Cooperation of Decision Procedures for the Satisfiability Problem

1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : 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.
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Cited literature [2 references]

https://hal.inria.fr/inria-00073939
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Submitted on : Wednesday, May 24, 2006 - 2:07:50 PM
Last modification on : Friday, February 4, 2022 - 3:31:27 AM
Long-term archiving on: : Monday, April 5, 2010 - 12:02:09 AM

### Identifiers

• HAL Id : inria-00073939, version 1

### Citation

Christophe Ringeissen. Cooperation of Decision Procedures for the Satisfiability Problem. [Research Report] RR-2753, INRIA. 1995, pp.19. ⟨inria-00073939⟩

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