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: https://drops.dagstuhl.de/opus/volltexte/2022/16859/
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Kenison, George

On the Skolem Problem for Reversible Sequences

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LIPIcs-MFCS-2022-61.pdf (0.7 MB)


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}
}

Keywords: The Skolem Problem, Linear Recurrences, Verification
Collection: 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)
Issue Date: 2022
Date of publication: 22.08.2022


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