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arXiv · 2512.09823

Weakly-unambiguous Parikh automata and their link to holonomic series

Alin Bostan·Arnaud Carayol·Florent Koechlin·Cyril Nicaud
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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 to its complexity.

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Alin Bostan, Arnaud Carayol, Florent Koechlin, Cyril Nicaud. 2025-12-10. Weakly-unambiguous Parikh automata and their link to holonomic series. https://doi.org/10.4230/lipics.icalp.2020.114

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