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NP Decision Procedure for Monomial and Linear Integer Constraints (2208.02713v2)

Published 4 Aug 2022 in cs.LO

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_jn (x_i <= x_jn). 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[Pn].

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