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
URL: https://drops.dagstuhl.de/opus/volltexte/2019/10697/
Molina Lovett, Antonio ; Shallit, Jeffrey
Optimal Regular Expressions for Permutations
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Abstract
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
@InProceedings{molinalovett_et_al:LIPIcs:2019:10697,
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 = {http://drops.dagstuhl.de/opus/volltexte/2019/10697},
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 | |
| Seminar: | 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019) | |
| Issue date: | 2019 | |
| Date of publication: | 04.07.2019 |
