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Documents authored by Guillon, Pierre

Document
Complete Volume
DOI: 10.4230/OASIcs.AUTOMATA.2021
OASIcs, Volume 90, AUTOMATA 2021, Complete Volume

Authors: Alonso Castillo-Ramirez, Pierre Guillon, and Kévin Perrot

Published in: OASIcs, Volume 90, 27th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2021)

Abstract
OASIcs, Volume 90, AUTOMATA 2021, Complete Volume
Cite as

27th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2021). Open Access Series in Informatics (OASIcs), Volume 90, pp. 1-186, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@Proceedings{castilloramirez_et_al:OASIcs.AUTOMATA.2021,
  title =	{{OASIcs, Volume 90, AUTOMATA 2021, Complete Volume}},
  booktitle =	{27th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2021)},
  pages =	{1--186},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-189-4},
  ISSN =	{2190-6807},
  year =	{2021},
  volume =	{90},
  editor =	{Castillo-Ramirez, Alonso and Guillon, Pierre and Perrot, K\'{e}vin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.AUTOMATA.2021},
  URN =		{urn:nbn:de:0030-drops-140087},
  doi =		{10.4230/OASIcs.AUTOMATA.2021},
  annote =	{Keywords: OASIcs, Volume 90, AUTOMATA 2021, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/OASIcs.AUTOMATA.2021.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Alonso Castillo-Ramirez, Pierre Guillon, and Kévin Perrot

Published in: OASIcs, Volume 90, 27th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2021)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

27th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2021). Open Access Series in Informatics (OASIcs), Volume 90, pp. 0:i-0:x, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{castilloramirez_et_al:OASIcs.AUTOMATA.2021.0,
  author =	{Castillo-Ramirez, Alonso and Guillon, Pierre and Perrot, K\'{e}vin},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{27th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2021)},
  pages =	{0:i--0:x},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-189-4},
  ISSN =	{2190-6807},
  year =	{2021},
  volume =	{90},
  editor =	{Castillo-Ramirez, Alonso and Guillon, Pierre and Perrot, K\'{e}vin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.AUTOMATA.2021.0},
  URN =		{urn:nbn:de:0030-drops-140092},
  doi =		{10.4230/OASIcs.AUTOMATA.2021.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.STACS.2021.32
Rice-Like Theorems for Automata Networks

Authors: Guilhem Gamard, Pierre Guillon, Kevin Perrot, and Guillaume Theyssier

Published in: LIPIcs, Volume 187, 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)

Abstract
We prove general complexity lower bounds on automata networks, in the style of Rice’s theorem, but in the computable world. Our main result is that testing any fixed first-order property on the dynamics of an automata network is either trivial, or NP-hard, or coNP-hard. Moreover, there exist such properties that are arbitrarily high in the polynomial-time hierarchy. We also prove that testing a first-order property given as input on an automata network (also part of the input) is PSPACE-hard. Besides, we show that, under a natural effectiveness condition, any nontrivial property of the limit set of a nondeterministic network is PSPACE-hard. We also show that it is PSPACE-hard to separate deterministic networks with a very high and a very low number of limit configurations; however, the problem of deciding whether the number of limit configurations is maximal up to a polynomial quantity belongs to the polynomial-time hierarchy.
Cite as

Guilhem Gamard, Pierre Guillon, Kevin Perrot, and Guillaume Theyssier. Rice-Like Theorems for Automata Networks. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 32:1-32:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{gamard_et_al:LIPIcs.STACS.2021.32,
  author =	{Gamard, Guilhem and Guillon, Pierre and Perrot, Kevin and Theyssier, Guillaume},
  title =	{{Rice-Like Theorems for Automata Networks}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{32:1--32:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.32},
  URN =		{urn:nbn:de:0030-drops-136770},
  doi =		{10.4230/LIPIcs.STACS.2021.32},
  annote =	{Keywords: Automata networks, Rice theorem, complexity classes, polynomial hierarchy, hardness}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2017.19
Comparison of Max-Plus Automata and Joint Spectral Radius of Tropical Matrices

Authors: Laure Daviaud, Pierre Guillon, and Glenn Merlet

Published in: LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

Abstract
Weighted automata over the tropical semiring Zmax are closely related to finitely generated semigroups of matrices over Zmax. In this paper, we use results in automata theory to study two quantities associated with sets of matrices: the joint spectral radius and the ultimate rank. We prove that these two quantities are not computable over the tropical semiring, i.e. there is no algorithm that takes as input a finite set of matrices S and provides as output the joint spectral radius (resp. the ultimate rank) of S. On the other hand, we prove that the joint spectral radius is nevertheless approximable and we exhibit restricted cases in which the joint spectral radius and the ultimate rank are computable. To reach this aim, we study the problem of comparing functions computed by weighted automata over the tropical semiring. This problem is known to be undecidable, and we prove that it remains undecidable in some specific subclasses of automata.
Cite as

Laure Daviaud, Pierre Guillon, and Glenn Merlet. Comparison of Max-Plus Automata and Joint Spectral Radius of Tropical Matrices. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 19:1-19:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{daviaud_et_al:LIPIcs.MFCS.2017.19,
  author =	{Daviaud, Laure and Guillon, Pierre and Merlet, Glenn},
  title =	{{Comparison of Max-Plus Automata and Joint Spectral Radius of Tropical Matrices}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{19:1--19:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.19},
  URN =		{urn:nbn:de:0030-drops-81052},
  doi =		{10.4230/LIPIcs.MFCS.2017.19},
  annote =	{Keywords: max-plus automata, max-plus matrices, weighted automata, tropical semiring, joint spectral radius, ultimate rank}
}
Document
DOI: 10.4230/LIPIcs.STACS.2010.2451
Ultimate Traces of Cellular Automata

Authors: Julien Cervelle, Enrico Formenti, and Pierre Guillon

Published in: LIPIcs, Volume 5, 27th International Symposium on Theoretical Aspects of Computer Science (2010)

Abstract
A cellular automaton (CA) is a parallel synchronous computing model, which consists in a juxtaposition of finite automata (cells) whose state evolves according to that of their neighbors. Its trace is the set of infinite words representing the sequence of states taken by some particular cell. In this paper we study the ultimate trace of CA and partial CA (a CA restricted to a particular subshift). The ultimate trace is the trace observed after a long time run of the CA. We give sufficient conditions for a set of infinite words to be the trace of some CA and prove the undecidability of all properties over traces that are stable by ultimate coincidence.
Cite as

Julien Cervelle, Enrico Formenti, and Pierre Guillon. Ultimate Traces of Cellular Automata. In 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 5, pp. 155-166, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{cervelle_et_al:LIPIcs.STACS.2010.2451,
  author =	{Cervelle, Julien and Formenti, Enrico and Guillon, Pierre},
  title =	{{Ultimate Traces of Cellular Automata}},
  booktitle =	{27th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{155--166},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-16-3},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{5},
  editor =	{Marion, Jean-Yves and Schwentick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2010.2451},
  URN =		{urn:nbn:de:0030-drops-24518},
  doi =		{10.4230/LIPIcs.STACS.2010.2451},
  annote =	{Keywords: Discrete dynamical systems, cellular automata, symbolic dynamics, sofic systems, formal languages, decidability}
}
Document
DOI: 10.4230/LIPIcs.STACS.2010.2474
Revisiting the Rice Theorem of Cellular Automata

Authors: Pierre Guillon and Gaétan Richard

Published in: LIPIcs, Volume 5, 27th International Symposium on Theoretical Aspects of Computer Science (2010)

Abstract
A cellular automaton is a parallel synchronous computing model, which consists in a juxtaposition of finite automata whose state evolves according to that of their neighbors. It induces a dynamical system on the set of configurations, \ie the infinite sequences of cell states. The limit set of the cellular automaton is the set of configurations which can be reached arbitrarily late in the evolution. In this paper, we prove that all properties of limit sets of cellular automata with binary-state cells are undecidable, except surjectivity. This is a refinement of the classical ``Rice Theorem'' that Kari proved on cellular automata with arbitrary state sets.
Cite as

Pierre Guillon and Gaétan Richard. Revisiting the Rice Theorem of Cellular Automata. In 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 5, pp. 441-452, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{guillon_et_al:LIPIcs.STACS.2010.2474,
  author =	{Guillon, Pierre and Richard, Ga\'{e}tan},
  title =	{{Revisiting the Rice Theorem of Cellular Automata}},
  booktitle =	{27th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{441--452},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-16-3},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{5},
  editor =	{Marion, Jean-Yves and Schwentick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2010.2474},
  URN =		{urn:nbn:de:0030-drops-24744},
  doi =		{10.4230/LIPIcs.STACS.2010.2474},
  annote =	{Keywords: Cellular automata, undecidability}
}
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