Unifying Büchi complementation constructions

Seth Fogarty, Orna Kupferman, Moshe Y. Vardi, Thomas Wilke

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

6 Scopus citations

Abstract

Complementation of Büchi automata, required for checking automata containment, is of major theoretical and practical interest in formal verification. We consider two recent approaches to complementation. The first is the rank-based approach of Kupferman and Vardi, which operates over a DAG that embodies all runs of the automaton. This approach is based on the observation that the vertices of this DAG can be ranked in a certain way, termed an odd ranking, iff all runs are rejecting. The second is the slice-based approach of Kähler and Wilke. This approach tracks levels of "split trees" - run trees in which only essential information about the history of each run is maintained. While the slice-based construction is conceptually simple, the complementing automata it generates are exponentially larger than those of the recent rank-based construction of Schewe, and it suffers from the difficulty of symbolically encoding levels of split trees. In this work we reformulate the slice-based approach in terms of run DAGs and preorders over states. In doing so, we begin to draw parallels between the rank-based and slice-based approaches. Through deeper analysis of the slice-based approach, we strongly restrict the nondeterminism it generates. We are then able to employ the slice-based approach to provide a new odd ranking, called a retrospective ranking, that is different from the one provided by Kupferman and Vardi. This new ranking allows us to construct a deterministic-in-the-limit rank-based automaton with a highly restricted transition function. Further, by phrasing the slice-based approach in terms of ranks, our approach affords a simple symbolic encoding and achieves Schewe's tight bound.

Original languageAmerican English
Title of host publicationComputer Science Logic 2011 - 25th International Workshop/20th Annual Conference of the EACSL, CSL 2011
Pages248-263
Number of pages16
DOIs
StatePublished - 2011
Event25th International Workshop on Computer Science Logic, CSL 2011/20th Annual Conference of the European Association for Computer Science Logic, EACSL - Bergen, Norway
Duration: 12 Sep 201115 Sep 2011

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume12
ISSN (Print)1868-8969

Conference

Conference25th International Workshop on Computer Science Logic, CSL 2011/20th Annual Conference of the European Association for Computer Science Logic, EACSL
Country/TerritoryNorway
CityBergen
Period12/09/1115/09/11

Keywords

  • Büchi automata
  • Complementation
  • Determinism in the limit
  • Ranks

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