Annals of Mathematics and Artificial Intelligence

, Volume 24, Issue 1, pp 51–67

Constraints and universal algebra

  • Peter Jeavons
  • David Cohen
  • Justin Pearson
Article

DOI: 10.1023/A:1018941030227

Cite this article as:
Jeavons, P., Cohen, D. & Pearson, J. Annals of Mathematics and Artificial Intelligence (1998) 24: 51. doi:10.1023/A:1018941030227

Abstract

In this paper we explore the links between constraint satisfaction problems and universal algebra. We show that a constraint satisfaction problem instance can be viewed as a pair of relational structures, and the solutions to the problem are then the structure preserving mappings between these two relational structures. We give a number of examples to illustrate how this framework can be used to express a wide variety of combinatorial problems, many of which are not generally considered as constraint satisfaction problems. We also show that certain key aspects of the mathematical structure of constraint satisfaction problems can be precisely described in terms of the notion of a Galois connection, which is a standard notion of universal algebra. Using this result, we obtain an algebraic characterisation of the property of minimality in a constraint satisfaction problem. We also obtain a similar algebraic criterion for determining whether or not a given set of solutions can be expressed by a constraint satisfaction problem with a given structure, or a given set of allowed constraint types.

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Peter Jeavons
    • 1
  • David Cohen
    • 1
  • Justin Pearson
    • 1
  1. 1.Department of Computer Science, Royal HollowayUniversity ofLondonUK