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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2023

Z-polyregular functions

Z-polyregular functions

Résumé

This paper introduces a robust class of functions from finite words to integers that we call Z-polyregular functions. We show that it admits natural characterizations in terms of logics, Z-rational expressions, Z-rational series and transducers. We then study two subclass membership problems. First, we show that the asymptotic growth rate of a function is computable, and corresponds to the minimal number of variables required to represent it using logical formulas. Second, we show that first-order definability of Z-polyregular functions is decidable. To show the latter, we introduce an original notion of residual transducer, and provide a semantic characterization based on aperiodicity.
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hal-04097227 , version 1 (15-05-2023)

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Thomas Colcombet, Gaëtan Douéneau-Tabot, Aliaume Lopez. Z-polyregular functions. 2023. ⟨hal-04097227⟩
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