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Combining Satisfiability Procedures for Unions of Theories with a Shared Counting Operator

Nicolini E., Ringeissen C., Rusinowitch M.

Fundamenta Informaticae

2011

Vol. 105, nr 1/2

163-187

We present some decidability results for the universal fragment of theories modeling data structures and endowed with arithmetic constraints. More precisely, all the theories taken into account extend a theory that constrains the function symbol for the successor. A general decision procedure is obtained, by devising an appropriate calculus based on superposition. Moreover, we derive a decidability result for the combination of the considered theories for data structures and some fragments of arithmetic by applying a general combination schema for theories sharing a common subtheory. The effectiveness of the resulting algorithm is ensured by using the proposed calculus and a careful adaptation of standard methods for reasoning about arithmetic, such as Gauss elimination, Fourier-Motzkin elimination and Groebner bases computation.

An open automated framework for constraint solver extension: the SoleX approach

Monfroy E., Ringeissen C.

Fundamenta Informaticae

1999

Vol. 39, Nr 1,2

167-187

In declarative programming languages based on the constraint programming paradigm, computations can be viewed as deductions enhanced with the use of constraint solvers. However, admissible constraints are restricted to formulae handled by solvers and thus, declarativity may be jeopardized. We propose a domain-independent scheme to extend constraint solvers so that they can handle alien constraints, i.e., constraint involving new function symbols. This mechanism, called SoleX, consists of a set of symbolic rule-based transformations: they add and deduce syntactical as well as semantic information related to alien constraints, complete the computation domain, and purify constraints in order to allow solvers to cope with alien constraints. These transformations can be seen as elementary solvers, and thus, SoleX is a collaboration of these several solvers with the initial solver. Some extensions of computation domains have already been studied to demonstrate the broad scope of SoleX potential applications.

Rule - based constraint programming

Kirchner C., Ringeissen C.

Fundamenta Informaticae

1998

Vol. 34, nr 3

225-262

In this paper we present a view of constraint programming based on the notion of rewriting controlled by strategies. We argue that this concept allows to describe in a unified way the constraint solving mechanism as well as the meta-language needed to manipulate the constraints. This has the advantage to provide descriptions that are very close to the proof theoretical setting used now to describe constraint manipulations like unification or numerical constraint solving. We examplify the approach by presenting examples of constraint solvers descriptions and combinations written in the ELAN language.