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.FSTTCS.2018.32
URN: urn:nbn:de:0030-drops-99315
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9931/
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Ganty, Pierre ; Gutiérrez, Elena

The Parikh Property for Weighted Context-Free Grammars

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Abstract

Parikh's Theorem states that every context-free grammar (CFG) is equivalent to some regular CFG when the ordering of symbols in the words is ignored. The same is not true for the so-called weighted CFGs, which additionally assign a weight to each grammar rule. If the result holds for a given weighted CFG G, we say that G satisfies the Parikh property. We prove constructively that the Parikh property holds for every weighted nonexpansive CFG. We also give a decision procedure for the property when the weights are over the rationals.

BibTeX - Entry

@InProceedings{ganty_et_al:LIPIcs:2018:9931,
  author =	{Pierre Ganty and Elena Guti{\'e}rrez},
  title =	{{The Parikh Property for Weighted Context-Free Grammars}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software  Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{32:1--32:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-093-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{122},
  editor =	{Sumit Ganguly and Paritosh Pandya},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9931},
  URN =		{urn:nbn:de:0030-drops-99315},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.32},
  annote =	{Keywords: Weighted Context-Free Grammars, Algebraic Language Theory, Parikh Image}
}

Keywords: Weighted Context-Free Grammars, Algebraic Language Theory, Parikh Image
Collection: 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)
Issue Date: 2018
Date of publication: 05.12.2018

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