License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2011.507
URN: urn:nbn:de:0030-drops-30396
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2011/3039/
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Freydenberger, Dominik D.

Extended Regular Expressions: Succinctness and Decidability

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Abstract

Most modern implementations of regular expression engines allow the use of variables (also called back references). The resulting extended regular expressions (which, in the literature, are also called practical regular expressions, rewbr, or regex) are able to express non-regular languages.

The present paper demonstrates that extended regular-expressions cannot be minimized effectively (neither with respect to length, nor number of variables), and that the tradeoff in size between extended and ``classical'' regular expressions is not bounded by any recursive function. In addition to this, we prove the undecidability of several decision problems (universality, equivalence, inclusion, regularity, and cofiniteness) for extended regular expressions. Furthermore, we show that all these results hold even if the extended regular expressions contain only a single variable.

BibTeX - Entry

@InProceedings{freydenberger:LIPIcs:2011:3039,
  author =	{Dominik D. Freydenberger},
  title =	{{Extended Regular Expressions: Succinctness and Decidability}},
  booktitle =	{28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011) },
  pages =	{507--518},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-25-5},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{9},
  editor =	{Thomas Schwentick and Christoph D{\"u}rr},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2011/3039},
  URN =		{urn:nbn:de:0030-drops-30396},
  doi =		{10.4230/LIPIcs.STACS.2011.507},
  annote =	{Keywords: extended regular expressions, regex, decidability, non-recursive tradeoffs}
}

Keywords: extended regular expressions, regex, decidability, non-recursive tradeoffs
Collection: 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)
Issue Date: 2011
Date of publication: 11.03.2011

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