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Universal Skolem Sets

The Skolem Problem asks to determine whether a given integer linear recurrence sequence (such as the Fibonacci numbers) has a zero term. This problem, whose decidability has been open for many decades, arises across a wide range of topics in computer science, including loop termination, probabilistic model checking, weighted automata theory, and dynamical systems, amongst many others. Recently, a new approach to the Skolem Problem was initiated via the notion of a Universal Skolem Set: a set S of natural numbers with the property that it is decidable, for any given linear recurrence sequence, whether the sequence has a zero in S. I will present a survey and overview of the Skolem Problem, including lines of attack based on Universal Skolem Sets.

This is joint work with Florian Luca, James Maynard, Armand Noubissie, and James Worrell.

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