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/
Luca, Florian ;
Ouaknine, Joël ;
Worrell, James
A Universal Skolem Set of Positive Lower Density
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: |
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Linear Recurrence Sequences, Skolem Problem, Exponential Diophantine Equations, Sieve Methods |
Collection: |
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47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022) |
Issue Date: |
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2022 |
Date of publication: |
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22.08.2022 |