Z-polyregular functions

被引：1

作者：

Colcombet, Thomas ^{[1
]}

Doueneau-Tabot, Gaetan ^{[1
,2
]}

Lopez, Aliaume ^{[1
,3
]}

机构：

[1] Univ Paris Cite, CNRS, IRIF, F-75013 Paris, France

[2] Direct Gen Armement Ingn Projets, Paris, France

[3] ENS Paris Saclay, CNRS, LMF, Paris, France

来源：

2023 38TH ANNUAL ACM/IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE, LICS | 2023年

关键词：

D O I：

10.1109/LICS56636.2023.10175685

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

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 firstorder 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.

引用

页数：13

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