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.ICALP.2020.114
URN: urn:nbn:de:0030-drops-125212
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12521/
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Bostan, Alin ; Carayol, Arnaud ; Koechlin, Florent ; Nicaud, Cyril

Weakly-Unambiguous Parikh Automata and Their Link to Holonomic Series

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Abstract

We investigate the connection between properties of formal languages and properties of their generating series, with a focus on the class of holonomic power series. We first prove a strong version of a conjecture by Castiglione and Massazza: weakly-unambiguous Parikh automata are equivalent to unambiguous two-way reversal bounded counter machines, and their multivariate generating series are holonomic. We then show that the converse is not true: we construct a language whose generating series is algebraic (thus holonomic), but which is inherently weakly-ambiguous as a Parikh automata language. Finally, we prove an effective decidability result for the inclusion problem for weakly-unambiguous Parikh automata, and provide an upper-bound on its complexity.

BibTeX - Entry

@InProceedings{bostan_et_al:LIPIcs:2020:12521,
  author =	{Alin Bostan and Arnaud Carayol and Florent Koechlin and Cyril Nicaud},
  title =	{{Weakly-Unambiguous Parikh Automata and Their Link to Holonomic Series}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{114:1--114:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Artur Czumaj and Anuj Dawar and Emanuela Merelli},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12521},
  URN =		{urn:nbn:de:0030-drops-125212},
  doi =		{10.4230/LIPIcs.ICALP.2020.114},
  annote =	{Keywords: generating series, holonomicity, ambiguity, reversal bounded counter machine, Parikh automata}
}

Keywords: generating series, holonomicity, ambiguity, reversal bounded counter machine, Parikh automata
Collection: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
Issue Date: 2020
Date of publication: 29.06.2020

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