The expressive power of valued constraints: hierarchies and collapses

Authors:
David A. Cohen;Peter G. Jeavons;Stanislav Živný
Affiliations:
Department of Computer Science, Royal Holloway, University of London, UK;Computing Laboratory, University of Oxford, UK;Computing Laboratory, University of Oxford, UK
Venue:
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Year:
2007

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Abstract

In this paper we investigate the ways in which a fixed collection of valued constraints can be combined to express other valued constraints. We show that in some cases a large class of valued constraints, of all possible arities, can be expressed by using valued constraints of a fixed finite arity. We also show that some simple classes of valued constraints, including the set of all monotonic valued constraints with finite cost values, cannot be expressed by a subset of any fixed finite arity, and hence form an infinite hierarchy.