Unifying Büchi Complementation Constructions

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dc.citation.firstpage1en_US
dc.citation.issueNumber1en_US
dc.citation.journalTitleLogical Methods in Computer Scienceen_US
dc.citation.lastpage26en_US
dc.citation.volumeNumber9en_US
dc.contributor.authorFogarty, Seth J.en_US
dc.contributor.authorKupferman, Ornaen_US
dc.contributor.authorWilke, Thomasen_US
dc.contributor.authorVardi, Moshe Y.en_US
dc.date.accessioned2017-07-31T18:12:33Zen_US
dc.date.available2017-07-31T18:12:33Zen_US
dc.date.issued2013en_US
dc.description.abstractComplementation of B\"uchi 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 K\"ahler 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 the tight bound of Schewe's constructionen_US
dc.identifier.citationFogarty, Seth J., Kupferman, Orna, Wilke, Thomas, et al.. "Unifying Büchi Complementation Constructions." <i>Logical Methods in Computer Science,</i> 9, no. 1 (2013) Epi Sciences: 1-26. http://dx.doi.org/10.2168/LMCS-9(1:13)2013.en_US
dc.identifier.digitalUnifying_Buchi_Complementation_Constructionsen_US
dc.identifier.doihttp://dx.doi.org/10.2168/LMCS-9(1:13)2013en_US
dc.identifier.urihttps://hdl.handle.net/1911/95632en_US
dc.language.isoengen_US
dc.publisherEpi Sciencesen_US
dc.rightsThis is an open-access article distributed under the terms of the Creative Commons Attribution-NoDerivs Licenseen_US
dc.rights.urihttps://creativecommons.org/licenses/by-nd/2.0/en_US
dc.titleUnifying Büchi Complementation Constructionsen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpublisher versionen_US
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