Universal Skolem Sets - Luca, Florian; Ouaknine, Joel; Worrell, James (Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science, 2021)
It is a longstanding open problem whether there is an algorithm to decide the Skolem Problem for linear recurrence sequences, namely whether a given such sequence has a zero term. In this paper we introduce the notion of a Universal Skolem Set: an infinite subset \mathcal{S} of the positive integers such that there is an effective procedure that inputs a linear recurrence sequence u = (u(n)) n ≥ 0 and decides whether u(n) = 0 for some n \in \mathcal{S}. The main technical contribution of the paper is to exhibit such a set.