No-Rainbow Problem and the Surjective Constraint Satisfaction Problem
Computational Complexity
2021-04-30 v4 Logic in Computer Science
Rings and Algebras
Abstract
The Surjective Constraint Satisfaction Problem (SCSP) is the problem of deciding whether there exists a surjective assignment to a set of variables subject to some specified constraints, where a surjective assignment is an assignment containing all elements of the domain. In this paper we show that the most famous SCSP, called No-Rainbow Problem, is NP-Hard. Additionally, we disprove the conjecture saying that the SCSP over a constraint language and the CSP over the same language with constants have the same computational complexity up to poly-time reductions. Our counter-example also shows that the complexity of the SCSP cannot be described in terms of polymorphisms of the constraint language.
Cite
@article{arxiv.2003.11764,
title = {No-Rainbow Problem and the Surjective Constraint Satisfaction Problem},
author = {Dmitriy Zhuk},
journal= {arXiv preprint arXiv:2003.11764},
year = {2021}
}