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Weakly-unambiguous Parikh automata and their link to holonomic series

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Alin Bostan
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Arnaud Carayol
Cyril Nicaud

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.
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Dates and versions

hal-03084639 , version 1 (21-12-2020)

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Alin Bostan, Arnaud Carayol, Florent Koechlin, Cyril Nicaud. Weakly-unambiguous Parikh automata and their link to holonomic series. ICALP 2020 - 47th International Colloquium on Automata, Languages and Programming, Jul 2020, Saarbrücken, Germany. pp.114.1-114.16, ⟨10.4230/LIPIcs.ICALP.2020.114⟩. ⟨hal-03084639⟩
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