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 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.
Keywords
Cite
@article{arxiv.2512.09823,
title = {Weakly-unambiguous Parikh automata and their link to holonomic series},
author = {Alin Bostan and Arnaud Carayol and Florent Koechlin and Cyril Nicaud},
journal= {arXiv preprint arXiv:2512.09823},
year = {2025}
}