Universal Skolem sets

Florian Luca, Joël Ouaknine, and James Worrell

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 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 ∈ S. The main technical contribution of the paper is to exhibit such a set.

Proceedings of LICS 21, 2021. 6 pages.
Distinguished Paper Award.

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