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  Cooperation of decision procedures for the satisfiability problem (1996) [23 citations — 4 self]

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by Christophe Ringeissen
Frontiers of Combining Systems: Proceedings of the 1st International Workshop, Munich (Germany), Applied Logic
ftp://ftp.loria.fr/pub/loria/protheo/COMMUNICATIONS_1996/Ringeissen-FroCos96.ps.gz
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Abstract:

Abstract. Constraint programming is strongly based on the use of solvers which are able to check satisability of constraints. We show in this paper a rule-based algorithm for solving in a modular way the satisability 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 dioeerent 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 simplies the understanding of the combination problem. The obtained decomposition algorithm is illustrated by the combination of non-disjoint equational theories. 1.

Citations

270 Simplification by cooperating decision procedures – Nelson, Oppen - 1979
168 Solving equations in abstract algebras: a rule-based survey of unification – Jouannaud, Kirchner - 1991
133 Deciding combinations of theories – Shostak - 1984
126 On the structure of abstract algebras – Birkhoff - 1935
104 Unification in the union of disjoint equational theories: Combining decision procedures – Baader, Schulz - 1996
86 Techniques for program verification – Nelson - 1981
66 A practical decision procedure for arithmetic with function symbols – Shostak - 1979
29 Combining symbolic constraint solvers on algebraic domains – Kirchner, Ringeissen - 1994
28 On the combination of symbolic constraints, solution domains, and constraint solvers – Baader, Schulz - 1995
27 Complexity, convexity and combinations of theories – Oppen - 1980
21 Combination Techniques and Decision Problems for Disunification – Baader, Schulz - 1995
18 Combination of constraint solving techniques: An algebraic point of view – Baader, Schulz - 1995
17 Combination of unification algorithms – Schmidt-Schau�� - 1989
15 Unification in a combination of equational theories with shared constants and its application to primal algebras – Ringeissen - 1992
9 Unification in combinations of collapse-free regular theories – Yelick - 1987
8 Unification in boolean rings and abelian groups – Boudet, Jouannaud, et al. - 1989
8 Combinaison de resolutions de contraintes'. These de Doctorat d'Universite, Universite Henri Poincare - Nancy 1 – Ringeissen - 1993
5 Combination techniques for nondisjoint equational theories – Ringeissen - 1994
5 First-Order Unification in Combinations of Equational Theories – Tid'en - 1986
5 Extending the CLP scheme to unions of constraint theories – Tinelli - 1995
3 Combination of Unification Algorithms in Equational Theories – Herold - 1987