Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2007.09099

A dichotomy theorem for nonuniform CSPs simplified

Andrei A. Bulatov
View original source ↗Read source document ↗Export metadata ↓

Abstract

In a non-uniform Constraint Satisfaction problem CSP(G), where G is a set of relations on a finite set A, the goal is to find an assignment of values to variables subject to constraints imposed on specified sets of variables using the relations from G. The Dichotomy Conjecture for the non-uniform CSP states that for every constraint language G the problem CSP(G) is either solvable in polynomial time or is NP-complete. It was proposed by Feder and Vardi in their seminal 1993 paper. In this paper we confirm the Dichotomy Conjecture.

Explore related subjects

cs.CCcs.LO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Andrei A. Bulatov. 2020-07-16. A dichotomy theorem for nonuniform CSPs simplified. https://arxiv.org/abs/2007.09099

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Graph Homomorphisms and Universal Algebra

Constraint satisfaction problems are computational problems that naturally appear in many areas of theoretical computer science. One of the central themes is their computational complexity, and in particular the border between polynomial-time tractability and NP-hardness. In this course we introduce the universal-algebraic approach to study the computational complexity of finite-domain CSPs. The course covers in particular the cyclic terms and bounded width theorems. To keep the presentation accessible, we start the course in the tangible setting of directed graphs and graph homomorphism problems.

cs.CC↗
arXiv2026

The Exact Growth Rate of Space-Optimal Reversible Pebbling on Chains

We determine the exact time exponent of space-optimal reversible pebbling on chains as $1.331742379256310\ldots$. The growth rate of space-optimal reach exists as a limit and admits a variational formula. The same exponent governs complete computations at minimal space, uniformly in the chain length.

cs.CC↗
arXiv2026

Randomized query complexity can beat certificate complexity

A long-standing open question in query complexity asks whether there is a total Boolean function f with R(f) << C(f), where R(f) and C(f) denote its bounded-error randomized query complexity and certificate complexity, respectively. We construct a function with R(f) = O~(sqrt{C(f)}), which is optimal up to log factors. The same function also has $Q(f) = O~(C(f)^{1/4}), where Q(f) is the bounded-error quantum query complexity of f, which is also nearly optimal.

cs.CC↗