On the Universal and Existential Fragments of the µ-Calculus.

Thomas A. Henzinger*, Orna Kupferman, Rupak Majumdar

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

6 Scopus citations

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 alternationfree 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.

Original languageEnglish
Title of host publicationTools and Algorithms for the Construction and Analysis of Systems
Subtitle of host publication9th International Conference, TACAS 2003, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2003, Warsaw, Poland, April 7-11, 2003, Proceedings
EditorsHubert Garavel, John Hatcliff
PublisherSpringer Verlag
Pages49-64
Number of pages16
ISBN (Print)3-540-00898-5
DOIs
StatePublished - 2003
Externally publishedYes
EventTools and Algorithms for the Construction and Analysis of Systems, 9th International Conference, TACAS 2003 - Warsaw, Poland
Duration: 7 Apr 200311 Apr 2003
Conference number: 9
https://vasy.inria.fr/tacas03/

Publication series

NameLecture Notes in Computer Science
Volume2619
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceTools and Algorithms for the Construction and Analysis of Systems, 9th International Conference, TACAS 2003
Country/TerritoryPoland
CityWarsaw
Period7/04/0311/04/03
Internet address

Bibliographical note

Funding Information:
A preliminary version of this paper appeared in the Proceedings of the 9th International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS 2003), Lecture Notes in Computer Science, vol. 2619, Springer, Berlin, 2003, pp. 49–64. This work was supported in part by NSF Grant CCR-9988172, the AFOSR MURI Grant F49620-00-1-0327, and a Microsoft Research Fellowship. ∗Corresponding author. E-mail address: [email protected] (R. Majumdar).

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