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.ICALP.2019.121
URN: urn:nbn:de:0030-drops-106978
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Molina Lovett, Antonio ; Shallit, Jeffrey

Optimal Regular Expressions for Permutations

LIPIcs-ICALP-2019-121.pdf (0.4 MB)


The permutation language P_n consists of all words that are permutations of a fixed alphabet of size n. Using divide-and-conquer, we construct a regular expression R_n that specifies P_n. We then give explicit bounds for the length of R_n, which we find to be 4^{n}n^{-(lg n)/4+Theta(1)}, and use these bounds to show that R_n has minimum size over all regular expressions specifying P_n.

BibTeX - Entry

  author =	{Antonio Molina Lovett and Jeffrey Shallit},
  title =	{{Optimal Regular Expressions for Permutations}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{121:1--121:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Christel Baier and Ioannis Chatzigiannakis and Paola Flocchini and Stefano Leonardi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-106978},
  doi =		{10.4230/LIPIcs.ICALP.2019.121},
  annote =	{Keywords: regular expressions, lower bounds, divide-and-conquer}

Keywords: regular expressions, lower bounds, divide-and-conquer
Collection: 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)
Issue Date: 2019
Date of publication: 04.07.2019

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