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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.

Dates et versions

hal-04284141 , version 1 (15-11-2023)

Identifiants

Citer

Thomas Colcombet, Gaëtan Douéneau-Tabot, Aliaume Lopez. ℤ-polyregular functions. 2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), Jun 2023, Boston, United States. pp.1-13, ⟨10.1109/LICS56636.2023.10175685⟩. ⟨hal-04284141⟩
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