eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2010-01-07
9441
1
14
10.4230/DagSemProc.09441.1
article
09441 Abstracts Collection – The Constraint Satisfaction Problem: Complexity and Approximability
Bulatov, Andrei A.
Grohe, Martin
Kolaitis, Phokion G.
Krokhin, Andrei
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.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol09441/DagSemProc.09441.1/DagSemProc.09441.1.pdf
Constraint satisfaction problem (CSP)
satisfiability
computational complexity
CSP dichotomy conjecture
hardness of approximation
unique games conjecture
universal algebra
logic
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2010-01-07
9441
1
2
10.4230/DagSemProc.09441.2
article
09441 Executive Summary – The Constraint Satisfaction Problem: Complexity and Approximability
Bulatov, Andrei A.
Grohe, Martin
Kolaitis, Phokion G.
Krokhin, Andrei
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.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol09441/DagSemProc.09441.2/DagSemProc.09441.2.pdf
Constraint satisfaction problem (CSP)
satisfiability
computational complexity
CSP dichotomy conjecture
hardness of approximation
unique games conjecture
universal algebra
logic
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2010-01-07
9441
1
20
10.4230/DagSemProc.09441.3
article
On the Expression Complexity of Equivalence and Isomorphism of Primitive Positive Formulas
Valeriote, Matt
Bova, Simone
Chen, Hubie
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.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol09441/DagSemProc.09441.3/DagSemProc.09441.3.pdf
Expression complexity
equivalence
isomorphism
primitive positive formulas
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2010-01-07
9441
1
15
10.4230/DagSemProc.09441.4
article
PP-DEFINABILITY IS CO-NEXPTIME-COMPLETE
Willard, Ross
$exists$-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.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol09441/DagSemProc.09441.4/DagSemProc.09441.4.pdf
Primitive positive formula
definability
complexity
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2010-01-07
9441
1
12
10.4230/DagSemProc.09441.5
article
The complexity of positive first-order logic without equality II: The four-element case
Martin, Barnaby
Martin, Jos
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.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol09441/DagSemProc.09441.5/DagSemProc.09441.5.pdf
Quantified constraints
Galois connection