License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2016.44
URN: urn:nbn:de:0030-drops-57453
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/5745/
Holub, Štepán ;
Shallit, Jeffrey
Periods and Borders of Random Words
Abstract
We investigate the behavior of the periods and border lengths of random words over a fixed alphabet. We show that the asymptotic probability that a random word has a given maximal border length k is a constant, depending only on k and the alphabet size l. We give a recurrence that allows us to determine these constants with any required precision. This also allows us to evaluate the expected period of a random word. For the binary case, the expected period is asymptotically about n-1.641. We also give explicit formulas for the probability that a random word is unbordered or has maximum border length one.
BibTeX - Entry
@InProceedings{holub_et_al:LIPIcs:2016:5745,
author = {{\v{S}}tep{\'a}n Holub and Jeffrey Shallit},
title = {{Periods and Borders of Random Words}},
booktitle = {33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
pages = {44:1--44:10},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-001-9},
ISSN = {1868-8969},
year = {2016},
volume = {47},
editor = {Nicolas Ollinger and Heribert Vollmer},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/5745},
URN = {urn:nbn:de:0030-drops-57453},
doi = {10.4230/LIPIcs.STACS.2016.44},
annote = {Keywords: random word, period, word border}
}
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Keywords: |
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random word, period, word border |
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Collection: |
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33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016) |
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Issue Date: |
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2016 |
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Date of publication: |
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16.02.2016 |
