License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2022.61
URN: urn:nbn:de:0030-drops-168590
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16859/
Kenison, George
On the Skolem Problem for Reversible Sequences
Abstract
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.
BibTeX - Entry
@InProceedings{kenison:LIPIcs.MFCS.2022.61,
author = {Kenison, George},
title = {{On the Skolem Problem for Reversible Sequences}},
booktitle = {47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
pages = {61:1--61:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-256-3},
ISSN = {1868-8969},
year = {2022},
volume = {241},
editor = {Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/16859},
URN = {urn:nbn:de:0030-drops-168590},
doi = {10.4230/LIPIcs.MFCS.2022.61},
annote = {Keywords: The Skolem Problem, Linear Recurrences, Verification}
}
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Keywords: |
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The Skolem Problem, Linear Recurrences, Verification |
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Collection: |
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47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022) |
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Issue Date: |
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2022 |
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Date of publication: |
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22.08.2022 |
