Dagstuhl Seminar Proceedings, Volume 9441
Dagstuhl Seminar Proceedings
DagSemProc
https://www.dagstuhl.de/dagpub/1862-4405
https://dblp.org/db/series/dagstuhl
1862-4405
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
9441
2010
https://drops.dagstuhl.de/entities/volume/DagSemProc-volume-9441
09441 Abstracts Collection – The Constraint Satisfaction Problem: Complexity and Approximability
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.
Constraint satisfaction problem (CSP)
satisfiability
computational complexity
CSP dichotomy conjecture
hardness of approximation
unique games conjecture
universal algebra
logic
1-14
Regular Paper
Andrei A.
Bulatov
Andrei A. Bulatov
Martin
Grohe
Martin Grohe
Phokion G.
Kolaitis
Phokion G. Kolaitis
Andrei
Krokhin
Andrei Krokhin
10.4230/DagSemProc.09441.1
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09441 Executive Summary – The Constraint Satisfaction Problem: Complexity and Approximability
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.
Constraint satisfaction problem (CSP)
satisfiability
computational complexity
CSP dichotomy conjecture
hardness of approximation
unique games conjecture
universal algebra
logic
1-2
Regular Paper
Andrei A.
Bulatov
Andrei A. Bulatov
Martin
Grohe
Martin Grohe
Phokion G.
Kolaitis
Phokion G. Kolaitis
Andrei
Krokhin
Andrei Krokhin
10.4230/DagSemProc.09441.2
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On the Expression Complexity of Equivalence and Isomorphism of Primitive Positive Formulas
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.
Expression complexity
equivalence
isomorphism
primitive positive formulas
1-20
Regular Paper
Matt
Valeriote
Matt Valeriote
Simone
Bova
Simone Bova
Hubie
Chen
Hubie Chen
10.4230/DagSemProc.09441.3
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PP-DEFINABILITY IS CO-NEXPTIME-COMPLETE
$exists$-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.
Primitive positive formula
definability
complexity
1-15
Regular Paper
Ross
Willard
Ross Willard
10.4230/DagSemProc.09441.4
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The complexity of positive first-order logic without equality II: The four-element case
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.
Quantified constraints
Galois connection
1-12
Regular Paper
Barnaby
Martin
Barnaby Martin
Jos
Martin
Jos Martin
10.4230/DagSemProc.09441.5
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