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Documents authored by Asarin, Eugene

Document
DOI: 10.4230/LIPIcs.FSTTCS.2023.10
Bandwidth of Timed Automata: 3 Classes

Authors: Eugene Asarin, Aldric Degorre, Cătălin Dima, and Bernardo Jacobo Inclán

Published in: LIPIcs, Volume 284, 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)

Abstract
Timed languages contain sequences of discrete events ("letters") separated by real-valued delays, they can be recognized by timed automata, and represent behaviors of various real-time systems. The notion of bandwidth of a timed language defined in [Jacobo Inclán et al., 2022] characterizes the amount of information per time unit, encoded in words of the language observed with some precision ε. In this paper, we identify three classes of timed automata according to the asymptotics of the bandwidth of their languages with respect to this precision ε: automata are either meager, with an O(1) bandwidth, normal, with a Θ(log(1/ε)) bandwidth, or obese, with Θ(1/ε) bandwidth. We define two structural criteria and prove that they partition timed automata into these 3 classes of bandwidth, implying that there are no intermediate asymptotic classes. The classification problem of a timed automaton is PSPACE-complete. Both criteria are formulated using morphisms from paths of the timed automaton to some finite monoids extending Puri’s orbit graphs; the proofs are based on Simon’s factorization forest theorem.
Cite as

Eugene Asarin, Aldric Degorre, Cătălin Dima, and Bernardo Jacobo Inclán. Bandwidth of Timed Automata: 3 Classes. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 10:1-10:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{asarin_et_al:LIPIcs.FSTTCS.2023.10,
  author =	{Asarin, Eugene and Degorre, Aldric and Dima, C\u{a}t\u{a}lin and Jacobo Incl\'{a}n, Bernardo},
  title =	{{Bandwidth of Timed Automata: 3 Classes}},
  booktitle =	{43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)},
  pages =	{10:1--10:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-304-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{284},
  editor =	{Bouyer, Patricia and Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2023.10},
  URN =		{urn:nbn:de:0030-drops-193838},
  doi =		{10.4230/LIPIcs.FSTTCS.2023.10},
  annote =	{Keywords: timed automata, information theory, bandwidth, entropy, orbit graphs, factorization forests}
}
Document
DOI: 10.4230/LIPIcs.STACS.2016.11
Entropy Games and Matrix Multiplication Games

Authors: Eugene Asarin, Julien Cervelle, Aldric Degorre, Catalin Dima, Florian Horn, and Victor Kozyakin

Published in: LIPIcs, Volume 47, 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)

Abstract
Two intimately related new classes of games are introduced and studied: entropy games (EGs) and matrix multiplication games (MMGs). An EG is played on a finite arena by two-and-a-half players: Despot, Tribune and the non-deterministic People. Despot wants to make the set of possible People's behaviors as small as possible, while Tribune wants to make it as large as possible. An MMG is played by two players that alternately write matrices from some predefined finite sets. One wants to maximize the growth rate of the product, and the other to minimize it. We show that in general MMGs are undecidable in quite a strong sense. On the positive side, EGs correspond to a subclass of MMGs, and we prove that such MMGs and EGs are determined, and that the optimal strategies are simple. The complexity of solving such games is in NP cap coNP.
Cite as

Eugene Asarin, Julien Cervelle, Aldric Degorre, Catalin Dima, Florian Horn, and Victor Kozyakin. Entropy Games and Matrix Multiplication Games. In 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 47, pp. 11:1-11:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{asarin_et_al:LIPIcs.STACS.2016.11,
  author =	{Asarin, Eugene and Cervelle, Julien and Degorre, Aldric and Dima, Catalin and Horn, Florian and Kozyakin, Victor},
  title =	{{Entropy Games and Matrix Multiplication Games}},
  booktitle =	{33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
  pages =	{11:1--11:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-001-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{47},
  editor =	{Ollinger, Nicolas and Vollmer, Heribert},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2016.11},
  URN =		{urn:nbn:de:0030-drops-57129},
  doi =		{10.4230/LIPIcs.STACS.2016.11},
  annote =	{Keywords: game theory, entropy, joint spectral radius}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2010.376
Two Size Measures for Timed Languages

Authors: Eugene Asarin and Aldric Degorre

Published in: LIPIcs, Volume 8, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)

Abstract
Quantitative properties of timed regular languages, such as information content (growth rate, entropy) are explored. The approach suggested by the same authors is extended to languages of timed automata with punctual (equalities) and non-punctual (non-equalities) transition guards. Two size measures for such languages are identified: mean dimension and volumetric entropy. The former is the linear growth rate of the dimension of the language; it is characterized as the spectral radius of a max-plus matrix associated to the automaton. The latter is the exponential growth rate of the volume of the language; it is characterized as the logarithm of the spectral radius of a matrix integral operator on some Banach space associated to the automaton. Relation of the two size measures to classical information-theoretic concepts is explored.
Cite as

Eugene Asarin and Aldric Degorre. Two Size Measures for Timed Languages. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010). Leibniz International Proceedings in Informatics (LIPIcs), Volume 8, pp. 376-387, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{asarin_et_al:LIPIcs.FSTTCS.2010.376,
  author =	{Asarin, Eugene and Degorre, Aldric},
  title =	{{Two Size Measures for Timed Languages}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)},
  pages =	{376--387},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-23-1},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{8},
  editor =	{Lodaya, Kamal and Mahajan, Meena},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2010.376},
  URN =		{urn:nbn:de:0030-drops-28793},
  doi =		{10.4230/LIPIcs.FSTTCS.2010.376},
  annote =	{Keywords: timed automata, entropy, mean dimension}
}
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