License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CONCUR.2016.24
URN: urn:nbn:de:0030-drops-61867
URL: https://drops.dagstuhl.de/opus/volltexte/2016/6186/
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Urabe, Natsuki ; Shimizu, Shunsuke ; Hasuo, Ichiro

Coalgebraic Trace Semantics for Buechi and Parity Automata

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Abstract

Despite its success in producing numerous general results on state-based dynamics, the theory of coalgebra has struggled to accommodate the Buechi acceptance condition---a basic notion in the
theory of automata for infinite words or trees. In this paper we present a clean answer to the question that builds on the "maximality" characterization of infinite traces (by Jacobs and Cirstea): the accepted language of a Buechi automaton is characterized by two commuting diagrams, one for a least homomorphism and the other for a greatest, much like in a system of (least and greatest) fixed-point equations. This characterization works uniformly for the nondeterministic branching and the probabilistic one; and for words and trees alike. We present our results in terms of the parity acceptance condition that generalizes Buechi's.

BibTeX - Entry

@InProceedings{urabe_et_al:LIPIcs:2016:6186,
  author =	{Natsuki Urabe and Shunsuke Shimizu and Ichiro Hasuo},
  title =	{{Coalgebraic Trace Semantics for Buechi and Parity Automata}},
  booktitle =	{27th International Conference on Concurrency Theory (CONCUR 2016)},
  pages =	{24:1--24:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-017-0},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{59},
  editor =	{Jos{\'e}e Desharnais and Radha Jagadeesan},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6186},
  URN =		{urn:nbn:de:0030-drops-61867},
  doi =		{10.4230/LIPIcs.CONCUR.2016.24},
  annote =	{Keywords: coalgebra, Buechi automaton, parity automaton, probabilistic automaton, tree automaton}
}

Keywords: coalgebra, Buechi automaton, parity automaton, probabilistic automaton, tree automaton
Collection: 27th International Conference on Concurrency Theory (CONCUR 2016)
Issue Date: 2016
Date of publication: 24.08.2016

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