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
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Holub, Štepán ; Shallit, Jeffrey

Periods and Borders of Random Words

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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

  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 =		{},
  URN =		{urn:nbn:de:0030-drops-57453},
  doi =		{10.4230/LIPIcs.STACS.2016.44},
  annote =	{Keywords: random word, period, word border}

Keywords: random word, period, word border
Collection: 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)
Issue Date: 2016
Date of publication: 16.02.2016

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