Constraint Satisfaction Problems around Skolem Arithmetic

We study interactions between Skolem Arithmetic and certain classes of Constraint Satisfaction Problems (CSPs). We revisit results of Glaßer et al. [17] 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;×), 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.