6 Search Results for "Durand, Bruno"

Document
DOI: 10.4230/LIPIcs.STACS.2019.23
Resource-Bounded Kolmogorov Complexity Provides an Obstacle to Soficness of Multidimensional Shifts

Authors: Julien Destombes and Andrei Romashchenko

Published in: LIPIcs, Volume 126, 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)

Abstract
We suggest necessary conditions of soficness of multidimensional shifts formulated in terms of resource-bounded Kolmogorov complexity. Using this technique we provide examples of effective and non-sofic shifts on Z^2 with very low block complexity: the number of globally admissible patterns of size n x n grows only as a polynomial in n.
Cite as

Julien Destombes and Andrei Romashchenko. Resource-Bounded Kolmogorov Complexity Provides an Obstacle to Soficness of Multidimensional Shifts. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 23:1-23:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{destombes_et_al:LIPIcs.STACS.2019.23,
  author =	{Destombes, Julien and Romashchenko, Andrei},
  title =	{{Resource-Bounded Kolmogorov Complexity Provides an Obstacle to Soficness of Multidimensional Shifts}},
  booktitle =	{36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
  pages =	{23:1--23:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-100-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{126},
  editor =	{Niedermeier, Rolf and Paul, Christophe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.23},
  URN =		{urn:nbn:de:0030-drops-102624},
  doi =		{10.4230/LIPIcs.STACS.2019.23},
  annote =	{Keywords: Sofic shifts, Block complexity, Kolmogorov complexity}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2017.5
On the Expressive Power of Quasiperiodic SFT

Authors: Bruno Durand and Andrei Romashchenko

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

Abstract
In this paper we study the shifts, which are the shift-invariant and topologically closed sets of configurations over a finite alphabet in Z^d. The minimal shifts are those shifts in which all configurations contain exactly the same patterns. Two classes of shifts play a prominent role in symbolic dynamics, in language theory and in the theory of computability: the shifts of finite type (obtained by forbidding a finite number of finite patterns) and the effective shifts (obtained by forbidding a computably enumerable set of finite patterns). We prove that every effective minimal shift can be represented as a factor of a projective subdynamics on a minimal shift of finite type in a bigger (by 1) dimension. This result transfers to the class of minimal shifts a theorem by M.Hochman known for the class of all effective shifts and thus answers an open question by E. Jeandel. We prove a similar result for quasiperiodic shifts and also show that there exists a quasiperiodic shift of finite type for which Kolmogorov complexity of all patterns of size n\times n is \Omega(n).
Cite as

Bruno Durand and Andrei Romashchenko. On the Expressive Power of Quasiperiodic SFT. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 5:1-5:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{durand_et_al:LIPIcs.MFCS.2017.5,
  author =	{Durand, Bruno and Romashchenko, Andrei},
  title =	{{On the Expressive Power of Quasiperiodic SFT}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{5:1--5:14},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.5},
  URN =		{urn:nbn:de:0030-drops-80985},
  doi =		{10.4230/LIPIcs.MFCS.2017.5},
  annote =	{Keywords: minimal SFT, tilings, quasiperiodicityIn this paper we study the shifts, which are the shift-invariant and topologically closed sets of configurations}
}
Document
DOI: 10.4230/LIPIcs.CSL.2012.485
Towards CERes in intuitionistic logic

Authors: Alexander Leitsch, Giselle Reis, and Bruno Woltzenlogel Paleo

Published in: LIPIcs, Volume 16, Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL (2012)

Abstract
Cut-elimination, introduced by Gentzen, plays an important role in automating the analysis of mathematical proofs. The removal of cuts corresponds to the elimination of intermediate statements (lemmas), resulting in an analytic proof. CERes is a method of cut-elimination by resolution that relies on global proof transformations, in contrast to reductive methods, which use local proof-rewriting transformations. By avoiding redundant operations, it obtains a speed-up over Gentzen's traditional method (and its variations). CERes has been successfully implemented and applied to mathematical proofs, and it is fully developed for classical logic (first and higher order), multi-valued logics and Gödel logic. But when it comes to mathematical proofs, intuitionistic logic also plays an important role due to its constructive characteristics and computational interpretation. This paper presents current developments on adapting the CERes method to intuitionistic sequent calculus LJ. First of all, we briefly describe the CERes method for classical logic and the problems that arise when extending the method to intuitionistic logic. Then, we present the solutions found for the mentioned problems for the subclass LJ- (the class of intuitionistic proofs of an end-sequent containing no strong quantifiers and no formula on the right). In addition, we explain, with an example, some ideas for improving the method and covering a bigger fragment of LJ proofs. Finally, we summarize the results and point the direction for future research.
Cite as

Alexander Leitsch, Giselle Reis, and Bruno Woltzenlogel Paleo. Towards CERes in intuitionistic logic. In Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 16, pp. 485-499, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{leitsch_et_al:LIPIcs.CSL.2012.485,
  author =	{Leitsch, Alexander and Reis, Giselle and Woltzenlogel Paleo, Bruno},
  title =	{{Towards CERes in intuitionistic logic}},
  booktitle =	{Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL},
  pages =	{485--499},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-42-2},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{16},
  editor =	{C\'{e}gielski, Patrick and Durand, Arnaud},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2012.485},
  URN =		{urn:nbn:de:0030-drops-36922},
  doi =		{10.4230/LIPIcs.CSL.2012.485},
  annote =	{Keywords: cut-elimination, resolution, LJ}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2010.13
Special tree-width and the verification of monadic second-order graph pr operties

Authors: Bruno Courcelle

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

Abstract
The model-checking problem for monadic second-order logic on graphs is fixed-parameter tractable with respect to tree-width and clique-width. The proof constructs finite deterministic automata from monadic second-order sentences, but this computation produces automata of hyper-exponential sizes, and this is not avoidable. To overcome this difficulty, we propose to consider particular monadic second-order graph properties that are nevertheless interesting for Graph Theory and to interpret automata instead of trying to compile them (joint work with I. Durand). For checking monadic second-order sentences written with edge set quantifications, the appropriate parameter is tree-width. We introduce special tree-width, a graph complexity measure between path-width and tree-width. The corresponding automata are easier to construct than those for tree-width.
Cite as

Bruno Courcelle. Special tree-width and the verification of monadic second-order graph pr operties. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010). Leibniz International Proceedings in Informatics (LIPIcs), Volume 8, pp. 13-29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{courcelle:LIPIcs.FSTTCS.2010.13,
  author =	{Courcelle, Bruno},
  title =	{{Special tree-width and the verification of monadic second-order graph pr operties}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)},
  pages =	{13--29},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2010.13},
  URN =		{urn:nbn:de:0030-drops-28494},
  doi =		{10.4230/LIPIcs.FSTTCS.2010.13},
  annote =	{Keywords: model-checking, monadic second-order logic, fixed-parameter tractability, special tree-width}
}
Document
DOI: 10.4230/LIPIcs.STACS.2008.1334
Structural aspects of tilings

Authors: Alexis Ballier, Bruno Durand, and Emmanuel Jeandal

Published in: LIPIcs, Volume 1, 25th International Symposium on Theoretical Aspects of Computer Science (2008)

Abstract
In this paper, we study the structure of the set of tilings produced by any given tile-set. For better understanding this structure, we address the set of finite patterns that each tiling contains. This set of patterns can be analyzed in two different contexts: the first one is combinatorial and the other topological. These two approaches have independent merits and, once combined, provide somehow surprising results. The particular case where the set of produced tilings is countable is deeply investigated while we prove that the uncountable case may have a completely different structure. We introduce a pattern preorder and also make use of Cantor-Bendixson rank. Our first main result is that a tile-set that produces only periodic tilings produces only a finite number of them. Our second main result exhibits a tiling with exactly one vector of periodicity in the countable case.
Cite as

Alexis Ballier, Bruno Durand, and Emmanuel Jeandal. Structural aspects of tilings. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 61-72, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{ballier_et_al:LIPIcs.STACS.2008.1334,
  author =	{Ballier, Alexis and Durand, Bruno and Jeandal, Emmanuel},
  title =	{{Structural aspects of tilings}},
  booktitle =	{25th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{61--72},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-06-4},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{1},
  editor =	{Albers, Susanne and Weil, Pascal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1334},
  URN =		{urn:nbn:de:0030-drops-13343},
  doi =		{10.4230/LIPIcs.STACS.2008.1334},
  annote =	{Keywords: Tiling, domino, patterns, tiling preorder, tiling structure}
}
Document
DOI: 10.4230/DagSemRep.377
Centennial Seminar on Kolmogorov Complexity and Applications (Dagstuhl Seminar 03181)

Authors: Bruno Durand, Leonid A. Levin, Wolfgang Merkle, Alexander Shen, and Paul M. B. Vitanyi

Published in: Dagstuhl Seminar Reports. Dagstuhl Seminar Reports, Volume 1 (2021)

Abstract
Cite as

Bruno Durand, Leonid A. Levin, Wolfgang Merkle, Alexander Shen, and Paul M. B. Vitanyi. Centennial Seminar on Kolmogorov Complexity and Applications (Dagstuhl Seminar 03181). Dagstuhl Seminar Report 377, pp. 1-6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2003)

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@TechReport{durand_et_al:DagSemRep.377,
  author =	{Durand, Bruno and Levin, Leonid A. and Merkle, Wolfgang and Shen, Alexander and Vitanyi, Paul M. B.},
  title =	{{Centennial Seminar on Kolmogorov Complexity and Applications (Dagstuhl Seminar 03181)}},
  pages =	{1--6},
  ISSN =	{1619-0203},
  year =	{2003},
  type = 	{Dagstuhl Seminar Report},
  number =	{377},
  institution =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemRep.377},
  URN =		{urn:nbn:de:0030-drops-152578},
  doi =		{10.4230/DagSemRep.377},
}
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