. Constraint satisfaction problems have wide application in artificial intelligence. They involve finding values for problem variables where the values must be consistent in that they satisfy restrictions on which combinations of values are allowed. Two standard techniques used in solving such problems are backtrack search and consistency inference. Conventional wisdom in the constraint satisfaction community suggests: 1) using consistency inference as preprocessing before search to prune values from consideration reduces subsequent search effort and 2) using consistency inference during search to prune values from consideration is best done at the limited level embodied in the forward checking algorithm. We present evidence contradicting both pieces of conventional wisdom, and suggesting renewed consideration of an approach which fully maintains arc consistency during backtrack search. 1 Introduction Constraint satisfaction problems (CSPs) involve finding values for prob...

Many problems can be expressed in terms of a numeric constraint satisfaction problem over finite or continuous domains (numeric CSP). The purpose of this paper is to show that the consistency techniques that have been developed for CSPs can be adapted to numeric CSPs. Since the numeric domains are ordered the underlying idea is to handle domains only by their bounds. The semantics that have been elaborated, plus the complexity analysis and good experimental results, confirm that these techniques can be used in real applications. 1

We describe the design and implementation of a finite domain constraint solver embedded in a Prolog system using an extended unification mechanism via attributed variables as a generic constraint interface. The solver is essentially a scheduler for indexicals, i.e. reactive functional rules encoding local consistency methods performing incremental constraint solving or entailment checking, and global constraints, i.e. general propagators which may use specialized algorithms to achieve a higher degree of consistency or better time and space complexity. The solver has an open-ended design: the user can introduce new constraints, either in terms of indexicals by writing rules in a functional notation, or as global constraints via a Prolog programming interface. Constraints defined in terms of indexicals can be linked to 0/1-variables modeling entailment; thus indexicals are used for constraint solving as well as for entailment testing. Constraints can be arbitrarily combined using the ...

This paper presents a general model for temporal reasoning that is capable of handling both qualitative and quantitative information. This model allows the representation and processing of many types of constraints discussed in the literature to date, including metric constraints (restricting the distance between time points) and qualitative, disjunctive constraints (specifying the relative position of temporal objects). Reasoning tasks in this unified framework are formulated as constraint satisfaction problems and are solved by traditional constraint satisfaction techniques, such as backtracking and path consistency. New classes of tractable problems are characterized, involving qualitative networks augmented by quantitative domain constraints, some of which can be solved in polynomial time using arc and path consistency. This work was supported in part by grants from the Air Force Office of Scientific Research, AFOSR 900136, and the National Science Foundation, IRI 8815522...

A global cardinality constraint (gcc) is specified in terms of a set of variables X = fx1 ; :::; xpg which take their values in a subset of V = fv1 ; :::; vdg. It constrains the number of times a value v i 2 V is assigned toavariable in X to be in an interval (l i ;c i ). Cardinality constraints have proved very useful in many real-life problems, suchas scheduling, timetabling, or resource allocation. A gcc is more general than a constraint of difference, which requires each interval to be #0; 1#. In this paper, we present an efficient way of implementing generalized arc consistency for a gcc. The algorithm we propose is based on a new theorem of flow theory. Its space complexity is O(#Xj#jVj) and its time complexity is O(jXj 2 #jVj). We also show how this algorithm can efficiently be combined with other filtering techniques.

Constraint networks are used more and more to solve combinatorial problems in real-life applications. Much activity is concentrated on improving the efficiency of finding a solution in a constraint network (the constraint satisfaction problem, CSP). Particularly, arc consistency caught many researchers' attention, involving the discovery of a large number of algorithms. And, for the last two years, it has been shown that maintaining arc consistency during search is a worthwhile approach. However, results on CSPs and on arc consistency are almost always limited to binary constraint networks. The CSP is no longer an academic problem, and it is time to deal with non-binary CSPs, as widely required in real world constraint solvers. This paper proposes a general schema to implement arc consistency on constraints of any arity when no specific algorithm is known. A first instantiation of the schema is presented here, which deals with constraints given by a predicate, by the set of forbidden c...

. The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computer-aided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design. Traditional methods treat SAT as a discrete, constrained decision problem. In recent years, many optimization methods, parallel algorithms, and practical techniques have been developed for solving SAT. In this survey, we present a general framework (an algorithm space) that integrates existing SAT algorithms into a unified perspective. We describe sequential and parallel SAT algorithms including variable splitting, resolution, local search, global optimization, mathematical programming, and practical SAT algorithms. We give performance evaluation of some existing SAT algorithms. Finally, we provide a set of practical applications of the sat...

General purpose truth maintenance systems have received considerable attention in the past few years. This paper discusses the functionality of truth maintenance systems and compares various existing algorithms. Applications and directions for future research are also discussed. Introduction In 1978 Jon Doyle wrote a masters thesis at the MIT AI Laboratory entitled "Truth Maintenance Systems for Problem Solving" [ Doyle, 1979 ] . In this thesis Doyle described an independent module called a truth maintenance system, or TMS, which maintained beliefs for general problem solving systems. In the twelve years since the appearance of Doyle's TMS a large body of literature has accumulated on truth maintenance. The seminal idea appears not to have been any particular technical mechanism but rather the general concept of an independent module for truth (or belief) maintenance. All truth maintenance systems manipulate proposition symbols and relationships between proposition symbols. I will use...

In reasoning tasks involving the maintenance of consistent databases (so-called QQconstraint networks/Q/Q), it is customary to enforce local consistency conditions in order to simplify the subsequent construction of a globally coherent model of the data. In this paper we present a relationship between the sizes of the variables' domains, the constraints' arity and the level of local consistency sufficient to ensure global consistency. Based on these parameters a new tractability classification of constraint networks is presented. We also show, based on this relationship, that any relation on bi-valued variables which is not representable by a network of binary constraints cannot be represented by networks with any number of hidden variables.

Constraint programming is newly flowering in industry. Several companies have recently started up to exploit the technology, and the number of industrial applications is now growing very quickly. This survey will seek, by examples,