Constraint Satisfaction Problems around Skolem Arithmetic
Computational Complexity
2015-04-17 v1 Logic in Computer Science
Abstract
We study interactions between Skolem Arithmetic and certain classes of Constraint Satisfaction Problems (CSPs). We revisit results of Glass er et al. in the context of CSPs and settle the major open question from that paper, finding a certain satisfaction problem on circuits to be decidable. This we prove using the decidability of Skolem Arithmetic. We continue by studying first-order expansions of Skolem Arithmetic without constants, (N;*), where * indicates multiplication, as CSPs. We find already here a rich landscape of problems with non-trivial instances that are in P as well as those that are NP-complete.
Cite
@article{arxiv.1504.04181,
title = {Constraint Satisfaction Problems around Skolem Arithmetic},
author = {Christian Glasser and Peter Jonsson and Barnaby Martin},
journal= {arXiv preprint arXiv:1504.04181},
year = {2015}
}