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.2022.73
URN: urn:nbn:de:0030-drops-168711
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16871/
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Luca, Florian ; Ouaknine, Joël ; Worrell, James

A Universal Skolem Set of Positive Lower Density

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LIPIcs-MFCS-2022-73.pdf (0.7 MB)

Abstract

The Skolem Problem asks to decide whether a given integer linear recurrence sequence (LRS) has a zero term. Decidability of this problem has been open for many decades, with little progress since the 1980s. Recently, a new approach was initiated via the notion of a Skolem set - a set of positive integers relative to which the Skolem Problem is decidable. More precisely, ? is a Skolem set for a class ℒ of integer LRS if there is an effective procedure that, given an LRS in ℒ, decides whether the sequence has a zero in ?. A recent work exhibited a Skolem set for the class of all LRS that, while infinite, had density zero. In the present work we construct a Skolem set of positive lower density for the class of simple LRS .

BibTeX - Entry

@InProceedings{luca_et_al:LIPIcs.MFCS.2022.73,
  author =	{Luca, Florian and Ouaknine, Jo\"{e}l and Worrell, James},
  title =	{{A Universal Skolem Set of Positive Lower Density}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{73:1--73:12},
  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/2022/16871},
  URN =		{urn:nbn:de:0030-drops-168711},
  doi =		{10.4230/LIPIcs.MFCS.2022.73},
  annote =	{Keywords: Linear Recurrence Sequences, Skolem Problem, Exponential Diophantine Equations, Sieve Methods}
}

Keywords: Linear Recurrence Sequences, Skolem Problem, Exponential Diophantine Equations, Sieve Methods
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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