@techreport{Zivny07:expressiveTR,
  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.",
  address = "Oxford, UK",
  author = "David A. Cohen and Peter G. Jeavons and Stanislav \v{Z}ivn\'y",
  institution = "Computing Laboratory, University of Oxford",
  month = "April",
  number = "RR-07-03",
  title = "The expressive power of valued constraints: hierarchies and collapses",
  url = "http://web.comlab.ox.ac.uk/oucl/publications/tr/RR-07-03.html",
  year = "2007",
}