2010-02-01, English, Article, Journal or magazine article edition: The variable hierarchy for the games [mu] -calculus. Belkhir, Walid; Santocanale, Luigi

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Physical Description
  • Magazine/​Journal article
Published
  • Elsevier B.V., 2010 Feb
Language
  • English

Edition details

Title
  • The variable hierarchy for the games [mu] -calculus.
Appears In
  • Annals of Pure and Applied Logic, v.161, no.5, 2010 Feb, p.690(18) (ISSN: 0168-0072)
Author
  • Belkhir, Walid
  • Santocanale, Luigi
Published
  • Elsevier B.V., 2010 Feb
Physical Description
  • Magazine/​Journal article
Subjects
Target Audience
  • Academic
Summary
  • To link to full-text access for this article, visit this link: http:/​/​dx.doi.org/​10.1016/​j.apal.2009.07.015 Byline: Walid Belkhir, Luigi Santocanale Abstract: Parity games are combinatorial representations of closed Boolean [mu]-terms. By adding to them draw positions, they have been organized by Arnold and Santocanale (2005, 2007) into a [mu]-calculus (Arnold, 2001) whose standard interpretation is over the class of all complete lattices. As done by Berwanger et al. (2002, 2005) for the propositional modal [mu]-calculus, it is possible to classify parity games into levels of a hierarchy according to the number of fixed-point variables. We ask whether this hierarchy collapses w.r.t. the standard interpretation. We answer this question negatively by providing, for each n[greater than or equal to]1, a parity game G.sub.n with these properties: it unravels to a [mu]-term built up with n fixed-point variables, it is not semantically equivalent to any game with strictly less than n-2 fixed-point variables. Author Affiliation: Laboratoire d'Informatique Fondamentale de Marseille, Universite de Provence, 39 rue F. Joliot Curie, 13453 Marseille Cedex 13, France Article Note: (miscellaneous) Communicated by Guest Editor (ESNL)
Terms of Use
  • COPYRIGHT 2010 Elsevier B.V.
Language
  • English
Database
  • Gale Academic OneFile
Identifier
  • 218406560

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