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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: https://drops.dagstuhl.de/opus/volltexte/2022/17433/
Koechlin, Florent
New Analytic Techniques for Proving the Inherent Ambiguity of Context-Free Languages
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: |
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Inherent ambiguity, Infinite ambiguity, Ambiguity, Generating series, Context-free languages, Bounded languages |
Collection: |
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42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022) |
Issue Date: |
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2022 |
Date of publication: |
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14.12.2022 |