On the universal and existential fragments of the mu-calculus Journal Article


Author(s): Henzinger, Thomas A; Kupferman, Orna; Majumdar, Ritankar S
Article Title: On the universal and existential fragments of the mu-calculus
Affiliation
Abstract: One source of complexity in the μ-calculus is its ability to specify an unbounded number of switches between universal (AX) and existential (EX) branching modes. We therefore study the problems of satisfiability, validity, model checking, and implication for the universal and existential fragments of the μ-calculus, in which only one branching mode is allowed. The universal fragment is rich enough to express most specifications of interest, and therefore improved algorithms are of practical importance. We show that while the satisfiability and validity problems become indeed simpler for the existential and universal fragments, this is, unfortunately, not the case for model checking and implication. We also show the corresponding results for the alternation-free fragment of the μ-calculus, where no alternations between least and greatest fixed points are allowed. Our results imply that efforts to find a polynomial-time model-checking algorithm for the μ-calculus can be replaced by efforts to find such an algorithm for the universal or existential fragment.
Keywords: model checking; automata and logic; μ-Calculus; satisfiability
Journal Title: Theoretical Computer Science
Volume: 354
Issue 2
ISSN: 0304-3975
Publisher: Elsevier  
Date Published: 2006-03-28
Start Page: 173
End Page: 186
DOI: 10.1016/j.tcs.2005.11.015
Open access: no
IST Austria Authors
  1. Thomas A. Henzinger
    415 Henzinger
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