Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-26T03:05:42.810Z Has data issue: false hasContentIssue false
  • English
  • Français

Mu-depth 3 is more than 2: a game-theoretic proof

Published online by Cambridge University Press:  30 March 2001

GIACOMO LENZI
GIACOMO LENZI
Affiliation:
LaBRI, Université Bordeaux I, 351, Cours de la Libération, F-33405 Talence cedex, France. Email: [email protected] Dip. Mat. Appl. ‘U.Dini’, Università di Pisa, Via Bonanno 25B, 56100 Pisa, Italia.
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider the propositional modal mu-calculus, a logic proposed by Kozen in 1983. In this logic two operators μ and v are present, which express the least and greatest fixpoints of monotone operators on sets. Bradfield in 1998 proved for any n the existence of a mu-calculus formula that requires n alternations of μ and v. In this paper we consider the particular case n = 3 and we exhibit a new formula requiring 3 alternations. Our proof is independent of the technique of Bradfield, and is based on a new kind of game on infinite trees.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 11 , Issue 2 , April 2001 , pp. 273 - 297
Copyright
2001 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)