Fair equivalence relations

Orna Kupferman, Nir Piterman, Moshe Y. Vardi

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

2 Scopus citations


Equivalence between designs is a fundamental notion in verification. The linear and branching approaches to verification induce different notions of equivalence. When the designs aremodeled by fair state-transition systems, equivalence in the linear paradigm corresponds to fair trace equivalence, and in the branching paradigm corresponds to fair bisimulation. In this work we study the expressive power of various types of fairness conditions. For the linear paradigm, it is known that the Büchi condition is sufficiently strong (that is, a fair system that uses Rabin or Streett fairness can be translated to an equivalent Büchi system). We show that in the branching paradigm the expressiveness hierarchy depends on the types of fair bisimulation one chooses to use. We consider three types of fair bisimulation studied in the literature: ∃-bisimulation, game-bisimulation, and ∀-bisimulation. We show that while gamebisimulation and ∀-bisimulation have the same expressiveness hierarchy as tree automata, ∃-bisimulation induces a different hierarchy. This hierarchy lies between the hierarchies of word and tree automata, and it collapses at Rabin conditions of index one, and Streett conditions of index two.

Original languageAmerican English
Title of host publicationFST TCS 2000
Subtitle of host publicationFoundations of Software Technology and Theoretical Computer Science - 20th Conference, Proceedings
EditorsSanjiv Kapoor, Sanjiva Prasad
PublisherSpringer Verlag
Number of pages13
ISBN (Print)3540414134, 9783540414131
StatePublished - 2000
Event20th Conference on Foundations of Software Technology and Theoretical Computer Science, FST TCS 2000 - New Delhi, India
Duration: 13 Dec 200015 Dec 2000

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference20th Conference on Foundations of Software Technology and Theoretical Computer Science, FST TCS 2000
CityNew Delhi

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2000.


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