Volume

Dagstuhl Seminar Proceedings, Volume 9441

Publication Details

  • published at: 2010-01-07
  • Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik

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Document
DOI: 10.4230/DagSemProc.09441.1
09441 Abstracts Collection – The Constraint Satisfaction Problem: Complexity and Approximability

Authors: Andrei A. Bulatov, Martin Grohe, Phokion G. Kolaitis, and Andrei Krokhin

Abstract
From 25th to 30th October 2009, the Dagstuhl Seminar 09441 ``The Constraint Satisfaction Problem: Complexity and Approximability'' 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.
Cite as

Andrei A. Bulatov, Martin Grohe, Phokion G. Kolaitis, and Andrei Krokhin. 09441 Abstracts Collection – The Constraint Satisfaction Problem: Complexity and Approximability. In The Constraint Satisfaction Problem: Complexity and Approximability. Dagstuhl Seminar Proceedings, Volume 9441, pp. 1-14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{bulatov_et_al:DagSemProc.09441.1,
  author =	{Bulatov, Andrei A. and Grohe, Martin and Kolaitis, Phokion G. and Krokhin, Andrei},
  title =	{{09441 Abstracts Collection – The Constraint Satisfaction Problem: Complexity and Approximability}},
  booktitle =	{The Constraint Satisfaction Problem: Complexity and Approximability},
  pages =	{1--14},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9441},
  editor =	{Andrei A. Bulatov and Martin Grohe and Phokion G. Kolaitis and Andrei Krokhin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09441.1},
  URN =		{urn:nbn:de:0030-drops-23710},
  doi =		{10.4230/DagSemProc.09441.1},
  annote =	{Keywords: Constraint satisfaction problem (CSP), satisfiability, computational complexity, CSP dichotomy conjecture, hardness of approximation, unique games conjecture, universal algebra, logic}
}
Document
DOI: 10.4230/DagSemProc.09441.2
09441 Executive Summary – The Constraint Satisfaction Problem: Complexity and Approximability

Authors: Andrei A. Bulatov, Martin Grohe, Phokion G. Kolaitis, and Andrei Krokhin

Abstract
The seminar brought together forty researchers from di®erent highly advanced areas of constraint satisfaction and with complementary ex- pertise (logical, algebraic, combinatorial, probabilistic aspects). The list of participants contained both senior and junior researchers and a small number of advanced graduate students.
Cite as

Andrei A. Bulatov, Martin Grohe, Phokion G. Kolaitis, and Andrei Krokhin. 09441 Executive Summary – The Constraint Satisfaction Problem: Complexity and Approximability. In The Constraint Satisfaction Problem: Complexity and Approximability. Dagstuhl Seminar Proceedings, Volume 9441, pp. 1-2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{bulatov_et_al:DagSemProc.09441.2,
  author =	{Bulatov, Andrei A. and Grohe, Martin and Kolaitis, Phokion G. and Krokhin, Andrei},
  title =	{{09441 Executive Summary – The Constraint Satisfaction Problem: Complexity and Approximability}},
  booktitle =	{The Constraint Satisfaction Problem: Complexity and Approximability},
  pages =	{1--2},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9441},
  editor =	{Andrei A. Bulatov and Martin Grohe and Phokion G. Kolaitis and Andrei Krokhin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09441.2},
  URN =		{urn:nbn:de:0030-drops-23706},
  doi =		{10.4230/DagSemProc.09441.2},
  annote =	{Keywords: Constraint satisfaction problem (CSP), satisfiability, computational complexity, CSP dichotomy conjecture, hardness of approximation, unique games conjecture, universal algebra, logic}
}
Document
DOI: 10.4230/DagSemProc.09441.3
On the Expression Complexity of Equivalence and Isomorphism of Primitive Positive Formulas

Authors: Matt Valeriote, Simone Bova, and Hubie Chen

Abstract
We study the complexity of equivalence and isomorphism on primitive positive formulas with respect to a given structure. We study these problems for various fixed structures; we present generic hardness and complexity class containment results, and give classification theorems for the case of two-element (boolean) structures.
Cite as

Matt Valeriote, Simone Bova, and Hubie Chen. On the Expression Complexity of Equivalence and Isomorphism of Primitive Positive Formulas. In The Constraint Satisfaction Problem: Complexity and Approximability. Dagstuhl Seminar Proceedings, Volume 9441, pp. 1-20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{valeriote_et_al:DagSemProc.09441.3,
  author =	{Valeriote, Matt and Bova, Simone and Chen, Hubie},
  title =	{{On the Expression Complexity of Equivalence and Isomorphism of Primitive Positive Formulas}},
  booktitle =	{The Constraint Satisfaction Problem: Complexity and Approximability},
  pages =	{1--20},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9441},
  editor =	{Andrei A. Bulatov and Martin Grohe and Phokion G. Kolaitis and Andrei Krokhin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09441.3},
  URN =		{urn:nbn:de:0030-drops-23690},
  doi =		{10.4230/DagSemProc.09441.3},
  annote =	{Keywords: Expression complexity, equivalence, isomorphism, primitive positive formulas}
}
Document
DOI: 10.4230/DagSemProc.09441.4
PP-DEFINABILITY IS CO-NEXPTIME-COMPLETE

Authors: Ross Willard

Abstract
$exists$-InvSat is the problem which takes as input a relation $R$ and a finite set $mathcal S$ of relations on the same finite domain $D$, and asks whether $R$ is definable by a conjunctive query over $mathcal S$, i.e., by a formula of the form $exists mathbf{y} varphi(mathbf{x},mathbf{y})$ where $varphi$ is a conjunction of atomic formulas built on the relations in $mathcal S cup {=}$. (These are also called emph{primitive positive formulas}.) The problem is known to be in co-NExpTime, and has been shown to be tractable on the boolean domain. We show that there exists $k>2$ such that $exists$-InvSat is co-NExpTime complete on $k$-element domains, answering a question of Creignou, Kolaitis and Zanuttini.
Cite as

Ross Willard. PP-DEFINABILITY IS CO-NEXPTIME-COMPLETE. In The Constraint Satisfaction Problem: Complexity and Approximability. Dagstuhl Seminar Proceedings, Volume 9441, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{willard:DagSemProc.09441.4,
  author =	{Willard, Ross},
  title =	{{PP-DEFINABILITY IS CO-NEXPTIME-COMPLETE}},
  booktitle =	{The Constraint Satisfaction Problem: Complexity and Approximability},
  pages =	{1--15},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9441},
  editor =	{Andrei A. Bulatov and Martin Grohe and Phokion G. Kolaitis and Andrei Krokhin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09441.4},
  URN =		{urn:nbn:de:0030-drops-23680},
  doi =		{10.4230/DagSemProc.09441.4},
  annote =	{Keywords: Primitive positive formula, definability, complexity}
}
Document
DOI: 10.4230/DagSemProc.09441.5
The complexity of positive first-order logic without equality II: The four-element case

Authors: Barnaby Martin and Jos Martin

Abstract
We study the complexity of evaluating positive equality-free sentences of first-order (FO) logic over fixed, finite structures B. This may be seen as a natural generalisation of the non-uniform quantified constraint satisfaction problem QCSP(B). Extending the algebraic methods of a previous paper, we derive a complete complexity classification for these problems as B ranges over structures of domain size 4. Specifically, each problem is either in Logspace, is NP-complete, is co-NP-complete or is Pspace-complete.
Cite as

Barnaby Martin and Jos Martin. The complexity of positive first-order logic without equality II: The four-element case. In The Constraint Satisfaction Problem: Complexity and Approximability. Dagstuhl Seminar Proceedings, Volume 9441, pp. 1-12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{martin_et_al:DagSemProc.09441.5,
  author =	{Martin, Barnaby and Martin, Jos},
  title =	{{The complexity of positive first-order logic without equality II: The four-element case}},
  booktitle =	{The Constraint Satisfaction Problem: Complexity and Approximability},
  pages =	{1--12},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9441},
  editor =	{Andrei A. Bulatov and Martin Grohe and Phokion G. Kolaitis and Andrei Krokhin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09441.5},
  URN =		{urn:nbn:de:0030-drops-23670},
  doi =		{10.4230/DagSemProc.09441.5},
  annote =	{Keywords: Quantified constraints, Galois connection}
}

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  • Bova, Simone
  • Bulatov, Andrei A.
  • C
  • Chen, Hubie
  • G
  • Grohe, Martin
  • K
  • Kolaitis, Phokion G.
  • Krokhin, Andrei
  • M
  • Martin, Barnaby
  • Martin, Jos
  • V
  • Valeriote, Matt
  • W
  • Willard, Ross

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