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Weakly-unambiguous Parikh automata and their link to holonomic series
Abstract : We investigate the connection between properties of formal languages and properties of their generating series, with a focus on the class of \emph{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.
https://hal.inria.fr/hal-03084639
Contributor : Alin Bostan Connect in order to contact the contributor
Submitted on : Monday, December 21, 2020 - 11:43:48 AM
Last modification on : Friday, January 14, 2022 - 3:42:02 AM
Contributor : Alin Bostan Connect in order to contact the contributor
Submitted on : Monday, December 21, 2020 - 11:43:48 AM
Last modification on : Friday, January 14, 2022 - 3:42:02 AM
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LIPIcs-ICALP-2020-114.pdf
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