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DOI: 10.4230/LIPIcs.CSL.2023.24

Explorable Automata

Authors: Emile Hazard and Denis Kuperberg

Published in: LIPIcs, Volume 252, 31st EACSL Annual Conference on Computer Science Logic (CSL 2023)

Abstract

We define the class of explorable automata on finite or infinite words. This is a generalization of History-Deterministic (HD) automata, where this time non-deterministic choices can be resolved by building finitely many simultaneous runs instead of just one. We show that recognizing HD parity automata of fixed index among explorable ones is in PTime, thereby giving a strong link between the two notions. We then show that recognizing explorable automata is ExpTime-complete, in the case of finite words or Büchi automata. Additionally, we define the notion of ω-explorable automata on infinite words, where countably many runs can be used to resolve the non-deterministic choices. We show that all reachability automata are ω-explorable, but this is not the case for safety ones. We finally show ExpTime-completeness for ω-explorability of automata on infinite words for the safety and co-Büchi acceptance conditions.

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Emile Hazard and Denis Kuperberg. Explorable Automata. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 24:1-24:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{hazard_et_al:LIPIcs.CSL.2023.24,
  author =	{Hazard, Emile and Kuperberg, Denis},
  title =	{{Explorable Automata}},
  booktitle =	{31st EACSL Annual Conference on Computer Science Logic (CSL 2023)},
  pages =	{24:1--24:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-264-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{252},
  editor =	{Klin, Bartek and Pimentel, Elaine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2023.24},
  URN =		{urn:nbn:de:0030-drops-174852},
  doi =		{10.4230/LIPIcs.CSL.2023.24},
  annote =	{Keywords: Nondeterminism, automata, complexity}
}

Document

DOI: 10.4230/LIPIcs.CSL.2022.23

Cyclic Proofs for Transfinite Expressions

Authors: Emile Hazard and Denis Kuperberg

Published in: LIPIcs, Volume 216, 30th EACSL Annual Conference on Computer Science Logic (CSL 2022)

Abstract

We introduce a cyclic proof system for proving inclusions of transfinite expressions, describing languages of words of ordinal length. We show that recognising valid cyclic proofs is decidable, that our system is sound and complete, and well-behaved with respect to cuts. Moreover, cyclic proofs can be effectively computed from expressions inclusions. We show how to use this to obtain a Pspace algorithm for transfinite expression inclusion.

Cite as

Emile Hazard and Denis Kuperberg. Cyclic Proofs for Transfinite Expressions. In 30th EACSL Annual Conference on Computer Science Logic (CSL 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 216, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{hazard_et_al:LIPIcs.CSL.2022.23,
  author =	{Hazard, Emile and Kuperberg, Denis},
  title =	{{Cyclic Proofs for Transfinite Expressions}},
  booktitle =	{30th EACSL Annual Conference on Computer Science Logic (CSL 2022)},
  pages =	{23:1--23:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-218-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{216},
  editor =	{Manea, Florin and Simpson, Alex},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2022.23},
  URN =		{urn:nbn:de:0030-drops-157433},
  doi =		{10.4230/LIPIcs.CSL.2022.23},
  annote =	{Keywords: transfinite expressions, transfinite automata, cyclic proofs}
}

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Documents authored by Hazard, Emile

Explorable Automata

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Cyclic Proofs for Transfinite Expressions

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