License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2022.41
URN: urn:nbn:de:0030-drops-174331
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17433/
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Koechlin, Florent

New Analytic Techniques for Proving the Inherent Ambiguity of Context-Free Languages

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Abstract

This article extends the work of Flajolet [Philippe Flajolet, 1987] on the relation between generating series and inherent ambiguity. We first propose an analytic criterion to prove the infinite inherent ambiguity of some context-free languages, and apply it to give a purely combinatorial proof of the infinite ambiguity of Shamir’s language. Then we show how Ginsburg and Ullian’s criterion on unambiguous bounded languages translates into a useful criterion on generating series, which generalises and simplifies the proof of the recent criterion of Makarov [Vladislav Makarov, 2021]. We then propose a new criterion based on generating series to prove the inherent ambiguity of languages with interlacing patterns, like {a^nb^ma^pb^q | n≠p or m≠q, with n,m,p,q ∈ ℕ^*}. We illustrate the applicability of these two criteria on many examples.

BibTeX - Entry

@InProceedings{koechlin:LIPIcs.FSTTCS.2022.41,
  author =	{Koechlin, Florent},
  title =	{{New Analytic Techniques for Proving the Inherent Ambiguity of Context-Free Languages}},
  booktitle =	{42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)},
  pages =	{41:1--41:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-261-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{250},
  editor =	{Dawar, Anuj and Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17433},
  URN =		{urn:nbn:de:0030-drops-174331},
  doi =		{10.4230/LIPIcs.FSTTCS.2022.41},
  annote =	{Keywords: Inherent ambiguity, Infinite ambiguity, Ambiguity, Generating series, Context-free languages, Bounded languages}
}

Keywords: Inherent ambiguity, Infinite ambiguity, Ambiguity, Generating series, Context-free languages, Bounded languages
Collection: 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)
Issue Date: 2022
Date of publication: 14.12.2022

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