Universal skolem sets
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...
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| Materiálatiipa: | Conference item |
| Giella: | English |
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IEEE
2021
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| Čoahkkáigeassu: | 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. |
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