A Logical Approach to Constraint Satisfaction

  • Authors:
  • Phokion G. Kolaitis;Moshe Y. Vardi

  • Affiliations:
  • IBM Almaden Research Center, Computer Science Principles and Methodologies and Computer Science Department, University of California, Santa Cruz,;Department of Computer Science, Rice University, Houston, TX 77005-1892

  • Venue:
  • Complexity of Constraints
  • Year:
  • 2008

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Abstract

Since the early 1970s, researchers in artificial intelligence (AI) have investigated a class of combinatorial problems that became known as constraint-satisfaction problems (CSP). The input to such a problem consists of a set of variables, a set of possible values for the variables, and a set of constraints between the variables; the question is to determine whether there is an assignment of values to the variables that satisfies the given constraints. The study of constraint satisfaction occupies a prominent place in artificial intelligence, because many problems that arise in different areas can be modelled as constraint-satisfaction problems in a natural way; these areas include Boolean satisfiability, temporal reasoning, belief maintenance, machine vision, and scheduling (cf. [Dec92a,Kum92,Mes89, Tsa93]). In its full generality, constraint satisfaction is an NP-complete problem. For this reason, researchers in artificial intelligence have pursued both heuristics for constraint-satisfaction problems and tractable cases obtained by imposing various restrictions on the input (cf. [MF93,Dec92a,DM94,Fro97,PJ97]).