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Dagstuhl Seminar Proceedings, Volume 10061

Publication Details

  • published at: 2010-04-26
  • Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik

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Document
DOI: 10.4230/DagSemProc.10061.1
10061 Abstracts Collection – Circuits, Logic, and Games

Authors: Benjamin Rossman, Thomas Schwentick, Denis Thérien, and Heribert Vollmer

Abstract
From 07/02/10 to 12/02/10, the Dagstuhl Seminar 10061 ``Circuits, Logic, and Games '' was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.
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Benjamin Rossman, Thomas Schwentick, Denis Thérien, and Heribert Vollmer. 10061 Abstracts Collection – Circuits, Logic, and Games. In Circuits, Logic, and Games. Dagstuhl Seminar Proceedings, Volume 10061, pp. 1-8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{rossman_et_al:DagSemProc.10061.1,
  author =	{Rossman, Benjamin and Schwentick, Thomas and Th\'{e}rien, Denis and Vollmer, Heribert},
  title =	{{10061 Abstracts Collection – Circuits, Logic, and Games}},
  booktitle =	{Circuits, Logic, and Games},
  pages =	{1--8},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10061},
  editor =	{Benjamin Rossman and Thomas Schwentick and Denis Th\'{e}rien and Heribert Vollmer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.10061.1},
  URN =		{urn:nbn:de:0030-drops-25280},
  doi =		{10.4230/DagSemProc.10061.1},
  annote =	{Keywords: Computational complexity theory, Finite model theory, Boolean circuits, Regular languages, Finite monoids, Ehrenfeucht-Fra\{\backslash''i\}ss\'{e}-games}
}
Document
DOI: 10.4230/DagSemProc.10061.2
10061 Executive Summary – Circuits, Logic, and Games

Authors: Benjamin Rossman, Thomas Schwentick, Denis Thérien, and Heribert Vollmer

Abstract
In the same way as during the first seminar on "Circuits, Logic, and Games"(Nov.~2006, 06451), the organizers aimed to bring together researchers from the areas of finite model theory and computational complexity theory, since they felt that perhaps not all developments in circuit theory and in logic had been explored fully in the context of lower bounds. In fact, the interaction between the areas has flourished a lot in the past 2-3 years, as can be exemplified by the following lines of research.
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Benjamin Rossman, Thomas Schwentick, Denis Thérien, and Heribert Vollmer. 10061 Executive Summary – Circuits, Logic, and Games. In Circuits, Logic, and Games. Dagstuhl Seminar Proceedings, Volume 10061, pp. 1-5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{rossman_et_al:DagSemProc.10061.2,
  author =	{Rossman, Benjamin and Schwentick, Thomas and Th\'{e}rien, Denis and Vollmer, Heribert},
  title =	{{10061 Executive Summary – Circuits, Logic, and Games}},
  booktitle =	{Circuits, Logic, and Games},
  pages =	{1--5},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10061},
  editor =	{Benjamin Rossman and Thomas Schwentick and Denis Th\'{e}rien and Heribert Vollmer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.10061.2},
  URN =		{urn:nbn:de:0030-drops-25279},
  doi =		{10.4230/DagSemProc.10061.2},
  annote =	{Keywords: Computational complexity theory, finite model theory, Boolean circuits, regular languages, finite monoids, Ehrenfeucht-Fra\backslash"\backslashi ss\backslash'e-games}
}
Document
DOI: 10.4230/DagSemProc.10061.3
Complexity Results for Modal Dependence Logic

Authors: Peter Lohmann and Heribert Vollmer

Abstract
Modal dependence logic was introduced very recently by Väänänen. It enhances the basic modal language by an operator dep. For propositional variables p_1,...,p_n, dep(p_1,...,p_(n-1);p_n) intuitively states that the value of p_n only depends on those of p_1,...,p_(n-1). Sevenster (J. Logic and Computation, 2009) showed that satisfiability for modal dependence logic is complete for nondeterministic exponential time. In this paper we consider fragments of modal dependence logic obtained by restricting the set of allowed propositional connectives. We show that satisfibility for poor man's dependence logic, the language consisting of formulas built from literals and dependence atoms using conjunction, necessity and possibility (i.e., disallowing disjunction), remains NEXPTIME-complete. If we only allow monotone formulas (without negation, but with disjunction), the complexity drops to PSPACE-completeness. We also extend Väänänen's language by allowing classical disjunction besides dependence disjunction and show that the satisfiability problem remains NEXPTIME-complete. If we then disallow both negation and dependence disjunction, satistiability is complete for the second level of the polynomial hierarchy. In this way we completely classify the computational complexity of the satisfiability problem for all restrictions of propositional and dependence operators considered by Väänänen and Sevenster.
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Peter Lohmann and Heribert Vollmer. Complexity Results for Modal Dependence Logic. In Circuits, Logic, and Games. Dagstuhl Seminar Proceedings, Volume 10061, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{lohmann_et_al:DagSemProc.10061.3,
  author =	{Lohmann, Peter and Vollmer, Heribert},
  title =	{{Complexity Results for Modal Dependence Logic}},
  booktitle =	{Circuits, Logic, and Games},
  pages =	{1--15},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10061},
  editor =	{Benjamin Rossman and Thomas Schwentick and Denis Th\'{e}rien and Heribert Vollmer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.10061.3},
  URN =		{urn:nbn:de:0030-drops-25240},
  doi =		{10.4230/DagSemProc.10061.3},
  annote =	{Keywords: Dependence logic, satisfiability problem, computational complexity, poor man's logic}
}
Document
DOI: 10.4230/DagSemProc.10061.4
Hardness of Parameterized Resolution

Authors: Olaf Beyersdorff, Nicola Galesi, and Massimo Lauria

Abstract
Parameterized Resolution and, moreover, a general framework for parameterized proof complexity was introduced by Dantchev, Martin, and Szeider (FOCS'07). In that paper, Dantchev et al. show a complexity gap in tree-like Parameterized Resolution for propositional formulas arising from translations of first-order principles. We broadly investigate Parameterized Resolution obtaining the following main results: 1) We introduce a purely combinatorial approach to obtain lower bounds to the proof size in tree-like Parameterized Resolution. For this we devise a new asymmetric Prover-Delayer game which characterizes proofs in (parameterized) tree-like Resolution. By exhibiting good Delayer strategies we then show lower bounds for the pigeonhole principle as well as the order principle. 2) Interpreting a well-known FPT algorithm for vertex cover as a DPLL procedure for Parameterized Resolution, we devise a proof search algorithm for Parameterized Resolution and show that tree-like Parameterized Resolution allows short refutations of all parameterized contradictions given as bounded-width CNF's. 3) We answer a question posed by Dantchev, Martin, and Szeider showing that dag-like Parameterized Resolution is not fpt-bounded. We obtain this result by proving that the pigeonhole principle requires proofs of size $n^{Omega(k)}$ in dag-like Parameterized Resolution. For this lower bound we use a different Prover-Delayer game which was developed for Resolution by Pudlák.
Cite as

Olaf Beyersdorff, Nicola Galesi, and Massimo Lauria. Hardness of Parameterized Resolution. In Circuits, Logic, and Games. Dagstuhl Seminar Proceedings, Volume 10061, pp. 1-28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{beyersdorff_et_al:DagSemProc.10061.4,
  author =	{Beyersdorff, Olaf and Galesi, Nicola and Lauria, Massimo},
  title =	{{Hardness of Parameterized Resolution}},
  booktitle =	{Circuits, Logic, and Games},
  pages =	{1--28},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10061},
  editor =	{Benjamin Rossman and Thomas Schwentick and Denis Th\'{e}rien and Heribert Vollmer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.10061.4},
  URN =		{urn:nbn:de:0030-drops-25254},
  doi =		{10.4230/DagSemProc.10061.4},
  annote =	{Keywords: Proof complexity, parameterized complexity, Resolution, Prover-Delayer Games}
}
Document
DOI: 10.4230/DagSemProc.10061.5
Proof Complexity of Propositional Default Logic

Authors: Olaf Beyersdorff, Arne Meier, Sebastian Müller, Michael Thomas, and Heribert Vollmer

Abstract
Default logic is one of the most popular and successful formalisms for non-monotonic reasoning. In 2002, Bonatti and Olivetti introduced several sequent calculi for credulous and skeptical reasoning in propositional default logic. In this paper we examine these calculi from a proof-complexity perspective. In particular, we show that the calculus for credulous reasoning obeys almost the same bounds on the proof size as Gentzen's system LK. Hence proving lower bounds for credulous reasoning will be as hard as proving lower bounds for LK. On the other hand, we show an exponential lower bound to the proof size in Bonatti and Olivetti's enhanced calculus for skeptical default reasoning.
Cite as

Olaf Beyersdorff, Arne Meier, Sebastian Müller, Michael Thomas, and Heribert Vollmer. Proof Complexity of Propositional Default Logic. In Circuits, Logic, and Games. Dagstuhl Seminar Proceedings, Volume 10061, pp. 1-14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{beyersdorff_et_al:DagSemProc.10061.5,
  author =	{Beyersdorff, Olaf and Meier, Arne and M\"{u}ller, Sebastian and Thomas, Michael and Vollmer, Heribert},
  title =	{{Proof Complexity of Propositional Default Logic}},
  booktitle =	{Circuits, Logic, and Games},
  pages =	{1--14},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10061},
  editor =	{Benjamin Rossman and Thomas Schwentick and Denis Th\'{e}rien and Heribert Vollmer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.10061.5},
  URN =		{urn:nbn:de:0030-drops-25261},
  doi =		{10.4230/DagSemProc.10061.5},
  annote =	{Keywords: Proof complexity, default logic, sequent calculus}
}
Document
DOI: 10.4230/DagSemProc.10061.6
The Complexity of Reasoning for Fragments of Autoepistemic Logic

Authors: Nadia Creignou, Arne Meier, Michael Thomas, and Heribert Vollmer

Abstract
Autoepistemic logic extends propositional logic by the modal operator L. A formula that is preceded by an L is said to be "believed". The logic was introduced by Moore 1985 for modeling an ideally rational agent's behavior and reasoning about his own beliefs. In this paper we analyze all Boolean fragments of autoepistemic logic with respect to the computational complexity of the three most common decision problems expansion existence, brave reasoning and cautious reasoning. As a second contribution we classify the computational complexity of counting the number of stable expansions of a given knowledge base. To the best of our knowledge this is the first paper analyzing the counting problem for autoepistemic logic.
Cite as

Nadia Creignou, Arne Meier, Michael Thomas, and Heribert Vollmer. The Complexity of Reasoning for Fragments of Autoepistemic Logic. In Circuits, Logic, and Games. Dagstuhl Seminar Proceedings, Volume 10061, pp. 1-10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{creignou_et_al:DagSemProc.10061.6,
  author =	{Creignou, Nadia and Meier, Arne and Thomas, Michael and Vollmer, Heribert},
  title =	{{The Complexity of Reasoning for Fragments of Autoepistemic Logic}},
  booktitle =	{Circuits, Logic, and Games},
  pages =	{1--10},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10061},
  editor =	{Benjamin Rossman and Thomas Schwentick and Denis Th\'{e}rien and Heribert Vollmer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.10061.6},
  URN =		{urn:nbn:de:0030-drops-25234},
  doi =		{10.4230/DagSemProc.10061.6},
  annote =	{Keywords: Autoepistemic logic, computational complexity, nonmonotonic reasoning, Post's lattice}
}

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  • Authors
  • B
  • Beyersdorff, Olaf
  • C
  • Creignou, Nadia
  • G
  • Galesi, Nicola
  • L
  • Lauria, Massimo
  • Lohmann, Peter
  • M
  • Meier, Arne
  • Müller, Sebastian
  • R
  • Rossman, Benjamin
  • S
  • Schwentick, Thomas
  • T
  • Thérien, Denis
  • Thomas, Michael
  • V
  • Vollmer, Heribert

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