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DOI: 10.4230/LIPIcs.ICALP.2020.114
URN: urn:nbn:de:0030-drops-125212
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12521/
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 | |
| Seminar: | 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020) | |
| Issue date: | 2020 | |
| Date of publication: | 29.06.2020 |
