Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Ciancia, Vincenzo; Venema, Yde https://www.dagstuhl.de/lipics License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
when quoting this document, please refer to the following
DOI:
URN: urn:nbn:de:0030-drops-114338
URL:

;

Omega-Automata: A Coalgebraic Perspective on Regular omega-Languages

pdf-format:


Abstract

In this work, we provide a simple coalgebraic characterisation of regular omega-languages based on languages of lassos, and prove a number of related mathematical results, framed into the theory of a new kind of automata called Omega-automata. In earlier work we introduced Omega-automata as two-sorted structures that naturally operate on lassos, pairs of words encoding ultimately periodic streams (infinite words). Here we extend the scope of these Omega-automata by proposing them as a new kind of acceptor for arbitrary streams. We prove that Omega-automata are expressively complete for the regular omega-languages. We show that, due to their coalgebraic nature, Omega-automata share some attractive properties with deterministic automata operating on finite words, properties that other types of stream automata lack. In particular, we provide a simple, coalgebraic definition of bisimilarity between Omega-automata that exactly captures language equivalence and allows for a simple minimization procedure. We also prove a coalgebraic Myhill-Nerode style theorem for lasso languages, and use this result, in combination with a closure property on stream languages called lasso determinacy, to give a characterization of regular omega-languages.

BibTeX - Entry

@InProceedings{ciancia_et_al:LIPIcs:2019:11433,
  author =	{Vincenzo Ciancia and Yde Venema},
  title =	{{Omega-Automata: A Coalgebraic Perspective on Regular omega-Languages}},
  booktitle =	{8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)},
  pages =	{5:1--5:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-120-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{139},
  editor =	{Markus Roggenbach and Ana Sokolova},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11433},
  URN =		{urn:nbn:de:0030-drops-114338},
  doi =		{10.4230/LIPIcs.CALCO.2019.5},
  annote =	{Keywords: omega-automata, regular omega-languages, coalgebra, streams, bisimilarity}
}

Keywords: omega-automata, regular omega-languages, coalgebra, streams, bisimilarity
Seminar: 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)
Issue date: 2019
Date of publication: 25.11.2019


DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI