2026-07-22T18:55:36Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:16859 2024-03-06T10:58:31Z ddc:004 open_access

On the Skolem Problem for Reversible Sequences Kenison, George The Skolem Problem Linear Recurrences Verification Given an integer linear recurrence sequence ⟨X_n⟩, the Skolem Problem asks to determine whether there is a natural number n such that X_n = 0. Recent work by Lipton, Luca, Nieuwveld, Ouaknine, Purser, and Worrell proved that the Skolem Problem is decidable for a class of reversible sequences of order at most seven. Here we give an alternative proof of their result. Our novel approach employs a powerful result for Galois conjugates that lie on two concentric circles due to Dubickas and Smyth. Schloss Dagstuhl – Leibniz-Zentrum für Informatik George Kenison 2022 Is Part Of LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2022.61 urn:nbn:de:0030-drops-168590 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.61 eng https://creativecommons.org/licenses/by/4.0/legalcode