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Documents authored by Duparc, Jacques

Document
DOI: 10.4230/LIPIcs.CSL.2015.534
On Unambiguous Regular Tree Languages of Index (0,2)

Authors: Jacques Duparc, Kevin Fournier, and Szczepan Hummel

Published in: LIPIcs, Volume 41, 24th EACSL Annual Conference on Computer Science Logic (CSL 2015)

Abstract
Unambiguous automata are usually seen as a natural class of automata in-between deterministic and nondeterministic ones. We show that in case of infinite tree languages, the unambiguous ones are topologically far more complicated than the deterministic ones. We do so by providing operations that generate a family (A_{alpha})_{alpha < phi_2(0)} of unambiguous automata such that: 1. It respects the strict Wadge ordering: alpha < beta if and only if A_{alpha} <_W A_{beta}. This can be established without the help of any determinacy principle, simply by providing effective winning strategies in the underlying games. 2. Its length (phi_2(0)) is the first fixpoint of the ordinal function that itself enumerates all fixpoints of the ordinal exponentiation x |-> omega^x: an ordinal tremendously larger than (omega^(omega))^3 +3 which is the height of the Wadge hierarchy of deterministic tree languages as uncovered by Filip Murlak. 3. The priorities of all these parity automata only range from 0 to 2.
Cite as

Jacques Duparc, Kevin Fournier, and Szczepan Hummel. On Unambiguous Regular Tree Languages of Index (0,2). In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 534-548, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{duparc_et_al:LIPIcs.CSL.2015.534,
  author =	{Duparc, Jacques and Fournier, Kevin and Hummel, Szczepan},
  title =	{{On Unambiguous Regular Tree Languages of Index (0,2)}},
  booktitle =	{24th EACSL Annual Conference on Computer Science Logic (CSL 2015)},
  pages =	{534--548},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-90-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{41},
  editor =	{Kreutzer, Stephan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2015.534},
  URN =		{urn:nbn:de:0030-drops-54369},
  doi =		{10.4230/LIPIcs.CSL.2015.534},
  annote =	{Keywords: Tree Automata, Unambiguity, Wadge Hierarchy.}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2011.363
Definable Operations On Weakly Recognizable Sets of Trees

Authors: Jacques Duparc, Alessandro Facchini, and Filip Murlak

Published in: LIPIcs, Volume 13, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)

Abstract
Alternating automata on infinite trees induce operations on languages which do not preserve natural equivalence relations, like having the same Mostowski--Rabin index, the same Borel rank, or being continuously reducible to each other (Wadge equivalence). In order to prevent this, alternation needs to be restricted to the choice of direction in the tree. For weak alternating automata with restricted alternation a small set of computable operations generates all definable operations, which implies that the Wadge degree of a given automaton is computable. The weak index and the Borel rank coincide, and are computable. An equivalent automaton of minimal index can be computed in polynomial time (if the productive states of the automaton are given).
Cite as

Jacques Duparc, Alessandro Facchini, and Filip Murlak. Definable Operations On Weakly Recognizable Sets of Trees. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 13, pp. 363-374, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{duparc_et_al:LIPIcs.FSTTCS.2011.363,
  author =	{Duparc, Jacques and Facchini, Alessandro and Murlak, Filip},
  title =	{{Definable Operations On Weakly Recognizable Sets of Trees}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)},
  pages =	{363--374},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-34-7},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{13},
  editor =	{Chakraborty, Supratik and Kumar, Amit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2011.363},
  URN =		{urn:nbn:de:0030-drops-33361},
  doi =		{10.4230/LIPIcs.FSTTCS.2011.363},
  annote =	{Keywords: alternating automata, Wadge hierarchy, index hierarchy}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2009.2312
The Wadge Hierarchy of Max-Regular Languages

Authors: Jérémie Cabessa, Jacques Duparc, Alessandro Facchini, and Filip Murlak

Published in: LIPIcs, Volume 4, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2009)

Abstract
Recently, Miko{\l}aj Boja{\'n}czyk introduced a class of max-regular languages, an extension of regular languages of infinite words preserving manyof its usual properties. This new class can be seen as a different way of generalising the notion of regularity from finite to infinite words. This paper compares regular and max-regular languages in terms of topological complexity.It is proved that up to Wadge equivalence the classes coincide. Moreover, when restricted to $\mathbf{\Delta}^0_2$-languages, the classes contain virtually the same languages. On the other hand, separating examples of arbitrary complexity exceeding $\mathbf{\Delta}^0_2$ are constructed.
Cite as

Jérémie Cabessa, Jacques Duparc, Alessandro Facchini, and Filip Murlak. The Wadge Hierarchy of Max-Regular Languages. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 121-132, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{cabessa_et_al:LIPIcs.FSTTCS.2009.2312,
  author =	{Cabessa, J\'{e}r\'{e}mie and Duparc, Jacques and Facchini, Alessandro and Murlak, Filip},
  title =	{{The Wadge Hierarchy of Max-Regular Languages}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{121--132},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-13-2},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{4},
  editor =	{Kannan, Ravi and Narayan Kumar, K.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2312},
  URN =		{urn:nbn:de:0030-drops-23122},
  doi =		{10.4230/LIPIcs.FSTTCS.2009.2312},
  annote =	{Keywords: Max-regular languages, Wadge hierarchy, Wagner hierarchy}
}
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