NP Decision Procedure for Monomial and Linear Integer Constraints
Logic in Computer Science
2022-10-21 v2
Abstract
Motivated by satisfiability of constraints with function symbols, we consider numerical inequalities on non-negative integers. The constraints we consider are a conjunction of a linear system Ax = b and a conjunction of (non-)convex constraints of the form x_i >= x_j^n (x_i <= x_j^n). We show that the satisfiability of these constraints is NP-complete even if the solution to the linear part is given explicitly. As a consequence, we obtain NP completeness for an extension of certain quantifier-free constraints on sets with cardinalities (QFBAPA) with function images S = f[P^n].
Cite
@article{arxiv.2208.02713,
title = {NP Decision Procedure for Monomial and Linear Integer Constraints},
author = {Rodrigo Raya and Jad Hamza and Viktor Kunčak},
journal= {arXiv preprint arXiv:2208.02713},
year = {2022}
}