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Documents authored by Arnold, André

Document
DOI: 10.4230/LIPIcs.CSL.2021.9
A Quasi-Polynomial Black-Box Algorithm for Fixed Point Evaluation

Authors: André Arnold, Damian Niwiński, and Paweł Parys

Published in: LIPIcs, Volume 183, 29th EACSL Annual Conference on Computer Science Logic (CSL 2021)

Abstract
We consider nested fixed-point expressions like μ z. ν y. μ x. f(x,y,z) evaluated over a finite lattice, and ask how many queries to a function f are needed to find the value. The previous upper bounds for a monotone function f of arity d over the lattice {0,1}ⁿ were of the order n^{𝒪(d)}, whereas a lower bound of Ω(n²/(lg n)) is known in case when at least one alternation between the least (μ) and the greatest (ν) fixed point occurs in the expression. Following a recent development for parity games, we show here that a quasi-polynomial number of queries is sufficient, namely n^{lg(d/lg n)+𝒪(1)}. The algorithm is an abstract version of several algorithms proposed recently by a number of authors, which involve (implicitly or explicitly) the structure of a universal tree. We then show a quasi-polynomial lower bound for the number of queries used by the algorithms in consideration.
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André Arnold, Damian Niwiński, and Paweł Parys. A Quasi-Polynomial Black-Box Algorithm for Fixed Point Evaluation. In 29th EACSL Annual Conference on Computer Science Logic (CSL 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 183, pp. 9:1-9:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{arnold_et_al:LIPIcs.CSL.2021.9,
  author =	{Arnold, Andr\'{e} and Niwi\'{n}ski, Damian and Parys, Pawe{\l}},
  title =	{{A Quasi-Polynomial Black-Box Algorithm for Fixed Point Evaluation}},
  booktitle =	{29th EACSL Annual Conference on Computer Science Logic (CSL 2021)},
  pages =	{9:1--9:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-175-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{183},
  editor =	{Baier, Christel and Goubault-Larrecq, Jean},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2021.9},
  URN =		{urn:nbn:de:0030-drops-134430},
  doi =		{10.4230/LIPIcs.CSL.2021.9},
  annote =	{Keywords: Mu-calculus, Parity games, Quasi-polynomial time, Black-box algorithm}
}
Document
DOI: 10.4230/LIPIcs.STACS.2012.396
On the separation question for tree languages

Authors: André Arnold, Henryk Michalewski, and Damian Niwinski

Published in: LIPIcs, Volume 14, 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)

Abstract
We show that the separation property fails for the classes Sigma_n of the Rabin-Mostowski index hierarchy of alternating automata on infinite trees. This extends our previous result (obtained with Szczepan Hummel) on the failure of the separation property for the class Sigma_2 (i.e., for co-Buchi sets). It remains open whether the separation property does hold for the classes Pi_n of the index hierarchy. To prove our result, we first consider the Rabin-Mostowski index hierarchy of deterministic automata on infinite words, for which we give a complete answer (generalizing previous results of Selivanov): the separation property holds for Pi_n and fails for Sigma_n-classes. The construction invented for words turns out to be useful for trees via a suitable game.
Cite as

André Arnold, Henryk Michalewski, and Damian Niwinski. On the separation question for tree languages. In 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 14, pp. 396-407, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{arnold_et_al:LIPIcs.STACS.2012.396,
  author =	{Arnold, Andr\'{e} and Michalewski, Henryk and Niwinski, Damian},
  title =	{{On the separation question for tree languages}},
  booktitle =	{29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)},
  pages =	{396--407},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-35-4},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{14},
  editor =	{D\"{u}rr, Christoph and Wilke, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2012.396},
  URN =		{urn:nbn:de:0030-drops-34156},
  doi =		{10.4230/LIPIcs.STACS.2012.396},
  annote =	{Keywords: Alternating automata on infinite trees, Index hierarchy, Separation property}
}
Document
DOI: 10.4230/DagSemRep.81
Algorithms in Automata Theory (Dagstuhl Seminar 9406)

Authors: André Arnold, Helmut Seidl, and Bernhard Steffen

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

Abstract
Cite as

André Arnold, Helmut Seidl, and Bernhard Steffen. Algorithms in Automata Theory (Dagstuhl Seminar 9406). Dagstuhl Seminar Report 81, pp. 1-28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (1994)

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@TechReport{arnold_et_al:DagSemRep.81,
  author =	{Arnold, Andr\'{e} and Seidl, Helmut and Steffen, Bernhard},
  title =	{{Algorithms in Automata Theory (Dagstuhl Seminar 9406)}},
  pages =	{1--28},
  ISSN =	{1619-0203},
  year =	{1994},
  type = 	{Dagstuhl Seminar Report},
  number =	{81},
  institution =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemRep.81},
  URN =		{urn:nbn:de:0030-drops-149691},
  doi =		{10.4230/DagSemRep.81},
}
Document
DOI: 10.4230/DagSemRep.54
Automata Theory: Distributed Models (Dagstuhl Seminar 9302)

Authors: André Arnold, Lutz Priese, and Roland Vollmer

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

Abstract
Cite as

André Arnold, Lutz Priese, and Roland Vollmer. Automata Theory: Distributed Models (Dagstuhl Seminar 9302). Dagstuhl Seminar Report 54, pp. 1-24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (1993)

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@TechReport{arnold_et_al:DagSemRep.54,
  author =	{Arnold, Andr\'{e} and Priese, Lutz and Vollmer, Roland},
  title =	{{Automata Theory: Distributed Models (Dagstuhl Seminar 9302)}},
  pages =	{1--24},
  ISSN =	{1619-0203},
  year =	{1993},
  type = 	{Dagstuhl Seminar Report},
  number =	{54},
  institution =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemRep.54},
  URN =		{urn:nbn:de:0030-drops-149422},
  doi =		{10.4230/DagSemRep.54},
}
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