# The expressive power of valued constraints: Hierarchies and collapses

*David A. Cohen‚ Peter G. Jeavons and Stanislav Živný*

### 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.

Journal

Theoretical Computer Science

Number

1

Pages

137–153

Volume

409

Year

2008