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Communication Dans Un Congrès Année : 2023

Z-polyregular functions

Résumé

This paper studies 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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Dates et versions

hal-04324059 , version 1 (05-12-2023)

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Thomas Colcombet, Gaëtan Douéneau-Tabot, Aliaume Lopez. Z-polyregular functions. 2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), IEEE, Jun 2023, Boston, United States. ⟨10.1109/LICS56636.2023.10175685⟩. ⟨hal-04324059⟩
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