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DOI: 10.4230/LIPIcs.STACS.2018.48
Computing the Longest Common Prefix of a Context-free Language in Polynomial Time

Authors: Michael Luttenberger, Raphaela Palenta, and Helmut Seidl

Published in: LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)

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.
Cite as

Michael Luttenberger, Raphaela Palenta, and Helmut Seidl. Computing the Longest Common Prefix of a Context-free Language in Polynomial Time. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 48:1-48:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{luttenberger_et_al:LIPIcs.STACS.2018.48,
  author =	{Luttenberger, Michael and Palenta, Raphaela and Seidl, Helmut},
  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 =	{Niedermeier, Rolf and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.48},
  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}
}
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