Results 1  10
of
22
Heterogeneous Constraint Solving
 PROCEEDINGS OF ALP'96, VOLUME 1139 OF LNCS
, 1996
"... Most CLP languages designed in the past few years feature at least some combination of constraint solving capabilities. These combinations can take multiple forms since they achieve either the mixing of di erent domains or the use of di erent algorithms over the same domain. These solvers are also v ..."
Abstract

Cited by 44 (10 self)
 Add to MetaCart
Most CLP languages designed in the past few years feature at least some combination of constraint solving capabilities. These combinations can take multiple forms since they achieve either the mixing of di erent domains or the use of di erent algorithms over the same domain. These solvers are also very di erent in nature. Some of them perform complete constraint solving while others are based on propagation methods. This paper is an attempt to design a uni ed framework describing the cooperation of constraint solving methods. Most techniques used in constraintbased systems are shown to be implementations of operators called constraint narrowing operators. A generalized notion of arcconsistency, called weak arcconsistency is proposed and is used to model heterogeneous constraint solving. We provide conditions on the constraint solving algorithms which guarantee termination, correctness and con uence of the resulting combined solver. This framework is shown to be general enough to describe the operational semantics of the basic constraint solving mechanisms in a number of current CLP systems. 1
Unions of NonDisjoint Theories and Combinations of Satisfiability Procedures
 THEORETICAL COMPUTER SCIENCE
, 2001
"... In this paper we outline a theoretical framework for the combination of decision procedures for constraint satisfiability. We describe a general combination method which, given a procedure that decides constraint satisfiability with respect to a constraint theory T1 and one that decides constraint s ..."
Abstract

Cited by 34 (3 self)
 Add to MetaCart
In this paper we outline a theoretical framework for the combination of decision procedures for constraint satisfiability. We describe a general combination method which, given a procedure that decides constraint satisfiability with respect to a constraint theory T1 and one that decides constraint satisfiability with respect to a constraint theory T2, produces a procedure that (semi)decides constraint satisfiability with respect to the union of T1 and T2. We provide a number of modeltheoretic conditions on the constraint language and the component constraint theories for the method to be sound and complete, with special emphasis on the case in which the signatures of the component theories are nondisjoint. We also describe some general classes of theories to which our combination results apply, and relate our approach to some of the existing combination methods in the field.
Constraint Satisfaction with Countable Homogeneous Templates
 IN PROCEEDINGS OF CSL’03
, 2003
"... For a fixed countable homogeneous structure we study the computational problem whether a given finite structure of the same relational signature homomorphically maps to . This problem is known as the constraint satisfaction problem CSP( ) for and was intensively studied for finite . We show that ..."
Abstract

Cited by 33 (15 self)
 Add to MetaCart
For a fixed countable homogeneous structure we study the computational problem whether a given finite structure of the same relational signature homomorphically maps to . This problem is known as the constraint satisfaction problem CSP( ) for and was intensively studied for finite . We show that  as in the case of finite  the computational complexity of CSP( ) for countable homogeneous is determinded by the clone of polymorphisms of . To this end we prove the following theorem which is of independent interest: The primitive positive definable relations over an !categorical structure are precisely the relations that are invariant under the polymorphisms of .
On the Combination of Symbolic Constraints, Solution Domains, and Constraint Solvers
 In Proceedings of the First International Conference on Principles and Practice of Constraint Programming
"... When combining languages for symbolic constraints, one is typically faced with the problem of how to treat "mixed" constraints. The two main problems are (1) how to define a combined solution structure over which these constraints are to be solved, and (2) how to combine the constraint solving metho ..."
Abstract

Cited by 26 (3 self)
 Add to MetaCart
When combining languages for symbolic constraints, one is typically faced with the problem of how to treat "mixed" constraints. The two main problems are (1) how to define a combined solution structure over which these constraints are to be solved, and (2) how to combine the constraint solving methods for pure constraints into one for mixed constraints. The paper introduces the notion of a "free amalgamated product" as a possible solution to the first problem. Subsequently, we define socalled simplycombinable structures (SCstructures). For SCstructures over disjoint signatures, a canonical amalgamation construction exists, which for the subclass of strong SCstructures yields the free amalgamated product. The combination technique of [BS92, BaS94a] can be used to combine constraint solvers for (strong) SCstructures over disjoint signatures into a solver for their (free) amalgamated product. In addition to term algebras modulo equational theories, the class of SCstru...
Implementing NonLinear Constraints With Cooperative Solvers
, 1995
"... We investigate the use of cooperation between solvers in the scheme of constraint logic programming languages over the domain of nonlinear polynomial constraints. Instead of using a general and often inefficient decision procedure we propose a new approach for handling these constraints by cooperat ..."
Abstract

Cited by 23 (12 self)
 Add to MetaCart
We investigate the use of cooperation between solvers in the scheme of constraint logic programming languages over the domain of nonlinear polynomial constraints. Instead of using a general and often inefficient decision procedure we propose a new approach for handling these constraints by cooperating specialised solvers. Our approach requires the design of a client/server architecture to enable communication between the various components. The main modules are a linear solver, a nonlinear solver, a constraint manager, a communication protocol component and an answer processor module. This work is motivated by the need for a declarative system for robot motion planning and geometric problem solving. We have implemented a prototype called CoSAc (Constraint System Architecture) to validate our approach using cooperating solvers for nonlinear constraints over the real numbers. Our language is illustrated by an example that also shows the advantages of cooperation.
Cooperation of Decision Procedures for the Satisfiability Problem
 Frontiers of Combining Systems: Proceedings of the 1st International Workshop, Munich (Germany), Applied Logic
, 1996
"... : Constraint programming is strongly based on the use of solvers which are able to check satisfiability of constraints. We show in this paper a rulebased 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 t ..."
Abstract

Cited by 22 (4 self)
 Add to MetaCart
: Constraint programming is strongly based on the use of solvers which are able to check satisfiability of constraints. We show in this paper a rulebased 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 nondeterministic decomposition algorithm but drastically simplifies the understanding of the combination problem. The obtained decomposition algorithm is illustrated by the combination of nondisjoint equational theories. Keywords: constraint programming, decision procedure, satisfiability, combination problem (R'esum'e : tsvp) INRIALorraine & CRIN, email: Christophe.Ringeissen@loria.fr Unit de recherche INRIA Lorraine Technpole de NancyBrabois, Campus scientifique, 615 rue de Jardin Botanique, BP 101, 54600 VILLE...
A New Approach for Combining Decision Procedures for the Word Problem, and Its Connection to the NelsonOppen Combination Method
 Proceedings of the 14th International Conference on Automated Deduction
, 1997
"... The NelsonOppen combination method can be used to combine decision procedures for the validity of quantifierfree formulae in firstorder theories with disjoint signatures, provided that the theories to be combined are stably infinite. We show that, even though equational theories need not sati ..."
Abstract

Cited by 21 (10 self)
 Add to MetaCart
The NelsonOppen combination method can be used to combine decision procedures for the validity of quantifierfree formulae in firstorder theories with disjoint signatures, provided that the theories to be combined are stably infinite. We show that, even though equational theories need not satisfy this property, Nelson and Oppen's method can be applied, after some minor modifications, to combine decision procedures for the validity of quantifierfree formulae in equational theories.
Combination of Constraint Solving Techniques: An Algebraic Point of View
 In Proceedings of the 6th International Conference on Rewriting Techniques and Applications, volume 914 of Lecture Notes in Computer Science
"... . In a previous paper we have introduced a method that allows one to combine decision procedures for unifiability in disjoint equational theories. Lately, it has turned out that the prerequisite for this method to applynamely that unification with socalled linear constant restrictions is dec ..."
Abstract

Cited by 16 (7 self)
 Add to MetaCart
. In a previous paper we have introduced a method that allows one to combine decision procedures for unifiability in disjoint equational theories. Lately, it has turned out that the prerequisite for this method to applynamely that unification with socalled linear constant restrictions is decidable in the single theoriesis equivalent to requiring decidability of the positive fragment of the first order theory of the equational theories. Thus, the combination method can also be seen as a tool for combining decision procedures for positive theories of free algebras defined by equational theories. Complementing this logical point of view, the present paper isolates an abstract algebraic property of free algebras called combinabilitythat clarifies why our combination method applies to such algebras. We use this algebraic point of view to introduce a new proof method that depends on abstract notions and results from universal algebra, as opposed to technical manipul...
The Constraint Solver Collaboration Language of BALI
 In Proceedings of the International Workshop Frontiers of Combining Systems, FroCoS'98
, 1998
"... In order to deal with constraint solvers integration, reusability, and cooperation, we have designed a domain independent environment for constraint solver collaboration (i.e., solver cooperation and solver combination) called BALI. This system allows one designing and implementing solver colla ..."
Abstract

Cited by 11 (6 self)
 Add to MetaCart
In order to deal with constraint solvers integration, reusability, and cooperation, we have designed a domain independent environment for constraint solver collaboration (i.e., solver cooperation and solver combination) called BALI. This system allows one designing and implementing solver collaborations with a highlevel language to compose solvers using collaboration primitives (such as sequentiality, concurrency and parallelism) and control primitives (such as iterator, fixedpoint and conditional). In this paper, we present the solver collaboration language of BALI, its operational semantics, some enrichments of the framework, an overview of the implementation, and some applications as well. 1 Introduction The need for solver collaboration, i.e., that is solver combination and cooperation, has been by now well recognized: several solvers collaborate to process constraints that cannot be solved (or efficiently solved) by a single solver. Informally, combination [ Nelson a...