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 \mathcal{S} of the positive integers...
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| Published in: | Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science pp. 1 - 6 |
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| Main Authors: | , , |
| Format: | Conference Proceeding |
| Language: | English |
| Published: |
IEEE
29.06.2021
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| Subjects: | |
| Online Access: | Get full text |
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| Summary: | 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. |
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| DOI: | 10.1109/LICS52264.2021.9470513 |