Constraint-based reasoning is a paradigm for formulating knowledge as a set of constraints without specifying the method by which these constraints are to be satisfied. A variety of techniques have been developed for finding partial or complete solutions for different kinds of constraint expressions. These have been successfully applied to diverse tasks such as design, diagnosis, truth maintenance, scheduling, spatiotemporal reasoning, logic programming and user interface. Constraint networks are graphical representations used to guide strategies for solving constraint satisfaction problems (CSPs).

In this paper we study the properties of the class of head-cycle-free extended disjunctive logic programs (HEDLPs), which includes, as a special case, all nondisjunctive extended logic programs. We show that any propositional HEDLP can be mapped in polynomial time into a propositional theory such that each model of the latter corresponds to an answer set, as defined by stable model semantics, of the former. Using this mapping, we show that many queries over HEDLPs can be determined by solving propositional satisfiability problems. Our mapping has several important implications: It establishes the NP-completeness of this class of disjunctive logic programs; it allows existing algorithms and tractable subsets for the satisfiability problem to be used in logic programming; it facilitates evaluation of the expressive power of disjunctive logic programs; and it leads to the discovery of useful similarities between stable model semantics and Clark's predicate completion. 1 Introduction ...

We compare tractable classes of constraint satisfaction problems (CSPs). We first give a uniform presentation of the major structural CSP decomposition methods. We then introduce a new class of tractable CSPs based on the concept of hypertree decomposition recently developed in Database Theory. We introduce a framework for comparing parametric decomposition-based methods according to tractability criteria and compare the most relevant methods. We show that the method of hypertree decomposition dominates the others in the case of general (nonbinary) CSPs.

. 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...

Many combinatorial search problems can be expressed as `constraint satisfaction problems', and this class of problems is known to be NP-complete in general. In this paper we investigate the subclasses which arise from restricting the possible constraint types. We first show that any set of constraints which does not give rise to an NP-complete class of problems must satisfy a certain type of algebraic closure condition. We then investigate all the different possible forms of this algebraic closure property, and establish which of these are sufficient to ensure tractability. As examples, we show that all known classes of tractable constraints over finite domains can be characterised by such an algebraic closure property. Finally, we describe a simple computational procedure which can be used to determine the closure properties of a given set of constraints. This procedure involves solving a particular constraint satisfaction problem, which we call an `indicator problem'. Keywords: Cons...

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...

We present in this paper a new, complete method for distributed constraint optimization, based on dynamic programming. It is a utility propagation method, inspired by the sum-product algorithm, which is correct only for tree-shaped constraint networks. In this paper, we show how to extend that algorithm to arbitrary topologies using a pseudotree arrangement of the problem graph. Our algorithm requires a linear number of messages, whose maximal size depends on the induced width along the particular pseudotree chosen. We compare our algorithm with backtracking algorithms, and present experimental results. For some problem types we report orders of magnitude fewer messages, and the ability to deal with arbitrarily large problems. Our algorithm is formulated for optimization problems, but can be easily applied to satisfaction problems as well.

Learning during backtrack search is a space-intensive process that records information (such as additional constraints) in order to avoid redundant work. In this paper, we analyze the effects of polynomial-spacebounded learning on runtime complexity of backtrack search. One space-bounded learning scheme records only those constraints with limited size, and another records arbitrarily large constraints but deletes those that become irrelevant to the portion of the search space being explored. We find that relevance-bounded learning allows better runtime bounds than size-bounded learning on structurally restricted constraint satisfaction problems. Even when restricted to linear space, our relevancebounded learning algorithm has runtime complexity near that of unrestricted (exponential space-consuming) learning schemes.

There is a very close relationship between constraint satisfaction problems and the satisfaction of join-dependencies in a relational database which is due to a common underlying structure, namely a hypergraph. By making that relationship explicit we are able to adapt techniques previously developed for the study of relational databases to obtain new results for constraint satisfaction problems. In particular, we prove that a constraint satisfaction problem may be decomposed into a number of subproblems precisely when the corresponding hypergraph satisfies a simple condition. We show that combining this decomposition approach with existing algorithms can lead to a significant improvement in efficiency.

We propose some global constraints for lexicographic orderings on vectors of variables. These constraints are very useful for breaking a certain kind of symmetry arising in matrices of decision variables. We show