@article{Zivny08:tcs,
  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.",
  author = "David A. Cohen and Peter G. Jeavons and Stanislav \v{Z}ivn\'y",
  doi = "10.1016/j.tcs.2008.08.036",
  journal = "Theoretical Computer Science",
  number = "1",
  pages = "137--153",
  title = "The expressive power of valued constraints: Hierarchies and collapses",
  url = "http://zivny.cz/publications/zj08cp.pdf",
  volume = "409",
  year = "2008",
}