# Continuity and Rational Functions

@inproceedings{Cadilhac2017ContinuityAR, title={Continuity and Rational Functions}, author={Micha{\"e}l Cadilhac and Olivier Carton and Charles Paperman}, booktitle={ICALP}, year={2017} }

A word-to-word function is continuous for a class of languages $\mathcal{V}$ if its inverse maps $\mathcal{V}$-languages to $\mathcal{V}$. This notion provides a basis for an algebraic study of transducers, and was integral to the characterization of the sequential transducers computable in some circuit complexity classes.
Here, we report on the decidability of continuity for functional transducers and some standard classes of regular languages. Previous algebraic studies of transducers have…

## 6 Citations

### Deciding the Computability of Regular Functions over Infinite Words

- MathematicsArXiv
- 2019

This paper establishes a generic characterisation of continuity for functions preserving regular languages under inverse image (such as regular functions) and exploits this characterisation to show the decidability of continuity of rational functions in NLogSpace, and of regular functions.

### Synthesis of Computable Regular Functions of Infinite Words

- Mathematics, Computer ScienceCONCUR
- 2020

This paper proposes a decision procedure for the following synthesis problem: given a regular function f, is f computable and if it is, synthesize a Turing machine computing it and effectively characterise uniform continuity of regular functions, and relates it to the notion of uniform computability, which offers stronger efficiency guarantees.

### Logical and Algebraic Characterizations of Rational Transductions

- Mathematics, Computer ScienceLog. Methods Comput. Sci.
- 2019

It is decidable if a rational transduction is first-order definable, and it is shown that this problem is PSPACE-complete.

### A pr 2 02 2 SYNTHESIS OF COMPUTABLE REGULAR FUNCTIONS OF INFINITE

- Mathematics, Computer Science
- 2022

This paper proposes a decision procedure for the following synthesis problem: given a regular function f, is f computable and if it is, synthesize a Turing machine computing it, and establishes a generic characterisation of continuity for functions preserving regular languages under inverse image.

### A Mahler's Theorem for Word Functions

- MathematicsICALP
- 2019

This work gives a construction process of all G_p preserving functions from a free monoid to a free group, a new noncommutative generalization of Mahler’s theorem on interpolation series.

### A NONCOMMUTATIVE EXTENSION OF MAHLER’S INTERPOLATION THEOREM

- Mathematics
- 2021

. We prove a noncommutative generalisation of Mahler’s theorem on interpolation series, a celebrated result of p -adic analysis. Mahler’s original result states that a function from N to Z is…

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