Network Satisfaction Problems Solved by k-Consistency
Abstract
We show that the problem of deciding for a given finite relation algebra A whether the network satisfaction problem for A can be solved by the k-consistency procedure, for some natural number k, is undecidable. For the important class of finite relation algebras A with a normal representation, however, the decidability of this problem remains open. We show that if A is symmetric and has a flexible atom, then the question whether NSP(A) can be solved by k-consistency, for some natural number k, is decidable (even in polynomial time in the number of atoms of A). This result follows from a more general sufficient condition for the correctness of the k-consistency procedure for finite symmetric relation algebras. In our proof we make use of a result of Alexandr Kazda about finite binary conservative structures.
Cite
@article{arxiv.2304.12871,
title = {Network Satisfaction Problems Solved by k-Consistency},
author = {Manuel Bodirsky and Simon Knäuer},
journal= {arXiv preprint arXiv:2304.12871},
year = {2025}
}
Comments
34 pages, 5 figures; a short version of this article is accepted for publication in the proceedings of ICALP 2023