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Coalgebraic Trace Semantics for Buechi and Parity Automata

Authors Natsuki Urabe, Shunsuke Shimizu, Ichiro Hasuo



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Natsuki Urabe
Shunsuke Shimizu
Ichiro Hasuo

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Natsuki Urabe, Shunsuke Shimizu, and Ichiro Hasuo. Coalgebraic Trace Semantics for Buechi and Parity Automata. In 27th International Conference on Concurrency Theory (CONCUR 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 59, pp. 24:1-24:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.CONCUR.2016.24

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.
Keywords
  • coalgebra
  • Buechi automaton
  • parity automaton
  • probabilistic automaton
  • tree automaton

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