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DOI: 10.4230/LIPIcs.STACS.2018.48
URN: urn:nbn:de:0030-drops-84828
URL: https://drops.dagstuhl.de/opus/volltexte/2018/8482/
Luttenberger, Michael ; Palenta, Raphaela ; Seidl, Helmut
Computing the Longest Common Prefix of a Context-free Language in Polynomial Time
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Abstract
We present two structural results concerning the longest common prefixes of non-empty languages.First, we show that the longest common prefix of the language generated by a context-free grammar of size N
equals the longest common prefix of the same grammar where the heights of the derivation trees are bounded by
4N.
Second, we show that each non-empty language L has a representative subset of at most three elements which behaves
like L w.r.t. the longest common prefix as well as w.r.t. longest common prefixes of L after unions or
concatenations with arbitrary other languages.
From that, we conclude
that the longest common prefix, and thus the longest common suffix, of a context-free language can be computed in polynomial time.
BibTeX - Entry
@InProceedings{luttenberger_et_al:LIPIcs:2018:8482,
author = {Michael Luttenberger and Raphaela Palenta and Helmut Seidl},
title = {{Computing the Longest Common Prefix of a Context-free Language in Polynomial Time}},
booktitle = {35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
pages = {48:1--48:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-062-0},
ISSN = {1868-8969},
year = {2018},
volume = {96},
editor = {Rolf Niedermeier and Brigitte Vall{\'e}e},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/8482},
URN = {urn:nbn:de:0030-drops-84828},
doi = {10.4230/LIPIcs.STACS.2018.48},
annote = {Keywords: longest common prefix, context-free languages, combinatorics on words}
}
| Keywords: | longest common prefix, context-free languages, combinatorics on words | |
| Seminar: | 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018) | |
| Issue date: | 2018 | |
| Date of publication: | 27.02.2018 |
