21,568 research outputs found
Necessary conditions for tractability of valued CSPs
The connection between constraint languages and clone theory has been a
fruitful line of research on the complexity of constraint satisfaction
problems. In a recent result, Cohen et al. [SICOMP'13] have characterised a
Galois connection between valued constraint languages and so-called weighted
clones. In this paper, we study the structure of weighted clones. We extend the
results of Creed and Zivny from [CP'11/SICOMP'13] on types of weightings
necessarily contained in every nontrivial weighted clone. This result has
immediate computational complexity consequences as it provides necessary
conditions for tractability of weighted clones and thus valued constraint
languages. We demonstrate that some of the necessary conditions are also
sufficient for tractability, while others are provably not.Comment: To appear in SIAM Journal on Discrete Mathematics (SIDMA
A Galois Connection for Weighted (Relational) Clones of Infinite Size
A Galois connection between clones and relational clones on a fixed finite
domain is one of the cornerstones of the so-called algebraic approach to the
computational complexity of non-uniform Constraint Satisfaction Problems
(CSPs). Cohen et al. established a Galois connection between finitely-generated
weighted clones and finitely-generated weighted relational clones [SICOMP'13],
and asked whether this connection holds in general. We answer this question in
the affirmative for weighted (relational) clones with real weights and show
that the complexity of the corresponding valued CSPs is preserved
A complexity dichotomy for poset constraint satisfaction
In this paper we determine the complexity of a broad class of problems that
extends the temporal constraint satisfaction problems. To be more precise we
study the problems Poset-SAT(), where is a given set of
quantifier-free -formulas. An instance of Poset-SAT() consists of
finitely many variables and formulas
with ; the question is
whether this input is satisfied by any partial order on or
not. We show that every such problem is NP-complete or can be solved in
polynomial time, depending on . All Poset-SAT problems can be formalized
as constraint satisfaction problems on reducts of the random partial order. We
use model-theoretic concepts and techniques from universal algebra to study
these reducts. In the course of this analysis we establish a dichotomy that we
believe is of independent interest in universal algebra and model theory.Comment: 29 page
Galois correspondence for counting quantifiers
We introduce a new type of closure operator on the set of relations,
max-implementation, and its weaker analog max-quantification. Then we show that
approximation preserving reductions between counting constraint satisfaction
problems (#CSPs) are preserved by these two types of closure operators.
Together with some previous results this means that the approximation
complexity of counting CSPs is determined by partial clones of relations that
additionally closed under these new types of closure operators. Galois
correspondence of various kind have proved to be quite helpful in the study of
the complexity of the CSP. While we were unable to identify a Galois
correspondence for partial clones closed under max-implementation and
max-quantification, we obtain such results for slightly different type of
closure operators, k-existential quantification. This type of quantifiers are
known as counting quantifiers in model theory, and often used to enhance first
order logic languages. We characterize partial clones of relations closed under
k-existential quantification as sets of relations invariant under a set of
partial functions that satisfy the condition of k-subset surjectivity. Finally,
we give a description of Boolean max-co-clones, that is, sets of relations on
{0,1} closed under max-implementations.Comment: 28 pages, 2 figure
- …