138 research outputs found
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
The number of clones determined by disjunctions of unary relations
We consider finitary relations (also known as crosses) that are definable via
finite disjunctions of unary relations, i.e. subsets, taken from a fixed finite
parameter set . We prove that whenever contains at least one
non-empty relation distinct from the full carrier set, there is a countably
infinite number of polymorphism clones determined by relations that are
disjunctively definable from . Finally, we extend our result to
finitely related polymorphism clones and countably infinite sets .Comment: manuscript to be published in Theory of Computing System
A Dichotomy Theorem for Polynomial Evaluation
A dichotomy theorem for counting problems due to Creignou and Hermann states
that or any nite set S of logical relations, the counting problem #SAT(S) is
either in FP, or #P-complete. In the present paper we show a dichotomy theorem
for polynomial evaluation. That is, we show that for a given set S, either
there exists a VNP-complete family of polynomials associated to S, or the
associated families of polynomials are all in VP. We give a concise
characterization of the sets S that give rise to "easy" and "hard" polynomials.
We also prove that several problems which were known to be #P-complete under
Turing reductions only are in fact #P-complete under many-one reductions
Algebra and the Complexity of Digraph CSPs: a Survey
We present a brief survey of some of the key results on the interplay between algebraic and graph-theoretic methods in the study of the complexity of digraph-based constraint satisfaction problems
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