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).

We view constraints as relations and constraint satisfaction as a dynamic process of approaching a stable equilibrium. We have developed an algebraic model of dynamics, called Constraint Nets, to provide a real-time programming semantics and to model and analyze dynamic systems. In this paper, we explore the relationship between constraint satisfaction and constraint nets by showing how to implement various constraint methods on constraint nets. 1 Motivation Constraints are relations among entities. Constraint satisfaction can be viewed in two different ways. First, in the logical deductive view, a constraint system is a structure hD; `i, where D is a set of constraints and ` is an entailment relation between constraints [20]. In this view, constraint satisfaction is seen as a process involving multiple agents concurrently interacting on the store-as-constraint system by checking entailment and consistency relations and refining the system monotonically. This approach is useful in da...

This paper explores the parallel complexity of finite constraint satisfaction problems (FCSPs) by developing three algorithms for deriving minimal constraint networks in parallel. The first is a parallel algorithm for the EREW PRAM model, the second is a distributed algorithm for fine-grain interconnected networks, and the third is a distributed algorithm for coarse-grain interconnected networks. Our major results are: given an FCSP represented by an acyclic constraint network (or a join tree) of size n with treewidth bounded by a constant, then (1) the parallel algorithm takes O(log n) time using O(n) processors, (2) there is an equivalent network, of size poly(n) with treewidth also bounded by a constant, which can be solved by the fine-grain distributed algorithm in O(log n) time using poly(n) processors and (3) the distributed algorithm for coarse-grain interconnected networks has linear speedup and linear scaleup. In addition, we have simulated the fine-grain distributed algorit...

This paper develops two new algorithms for solving a nite constraint satisfaction problem (FCSP) in parallel. In particular, we give a parallel algorithm for the EREW PRAM model and a distributed algorithm for networks of interconnected processors. Both of these algorithms are derived from arc consistency algorithms which are preprocessing algorithms in general, but can be used to solve anFCSP when it is represented by an acyclic constraint network. If an FCSP can be represented by an acyclic constraint network of size n with width bounded by a constant then (1) the parallel algorithm takes O(log n) time using O(n) processors and (2) there is a mapping of this problem to a distributed computing network of poly(n) processors which stabilizes in O(log n) time.

This paper presents a new way to map a Constraint Satisfaction Problem (CSP) onto a non-cooperative game. Constraint Satisfaction Problems arise in many areas of Artificial Intelligence and have usually been tackled with backtracking based algorithms. The relevance of equilibrium theory in games with respect to the problem of finding a solution or a partial solution for a CSP is shown. The concepts of Nash equilibrium, admissible equilibrium and perfect equilibrium are examined. We prove that the solutions of a CSP are equilibrium points in pure strategy, both in the sense of Nash and in the sense of Selten. Finally, it is shown a CSP solution can be reached through a step by step evolutionary process, in which variables update the probability of assuming a value, considering what the other variables will do. Some computer experiments are reported in the paper. 1 Introduction Artificial intelligence (AI) has started to look very closely at game theory in the last years. Many typical a...