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License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2021.123
URN: urn:nbn:de:0030-drops-141928
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14192/
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Casares, Antonio ; Colcombet, Thomas ; Fijalkow, Nathanaël

Optimal Transformations of Games and Automata Using Muller Conditions

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LIPIcs-ICALP-2021-123.pdf (0.8 MB)

Abstract

We consider the following question: given an automaton or a game with a Muller condition, how can we efficiently construct an equivalent one with a parity condition? There are several examples of such transformations in the literature, including in the determinisation of Büchi automata.
We define a new transformation called the alternating cycle decomposition, inspired and extending Zielonka’s construction. Our transformation operates on transition systems, encompassing both automata and games, and preserves semantic properties through the existence of a locally bijective morphism. We show a strong optimality result: the obtained parity transition system is minimal both in number of states and number of priorities with respect to locally bijective morphisms.
We give two applications: the first is related to the determinisation of Büchi automata, and the second is to give crisp characterisations on the possibility of relabelling automata with different acceptance conditions.

BibTeX - Entry

@InProceedings{casares_et_al:LIPIcs.ICALP.2021.123,
  author =	{Casares, Antonio and Colcombet, Thomas and Fijalkow, Nathana\"{e}l},
  title =	{{Optimal Transformations of Games and Automata Using Muller Conditions}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{123:1--123:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14192},
  URN =		{urn:nbn:de:0030-drops-141928},
  doi =		{10.4230/LIPIcs.ICALP.2021.123},
  annote =	{Keywords: Automata over infinite words, Omega regular languages, Determinisation of automata}
}

Keywords: Automata over infinite words, Omega regular languages, Determinisation of automata
Collection: 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)
Issue Date: 2021
Date of publication: 02.07.2021

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