# 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}
}
• Published in ICALP 28 February 2018
• Mathematics
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

• Mathematics
ArXiv
• 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 Science
CONCUR
• 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 Science
Log. 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

• Mathematics
ICALP
• 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

. 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

## References

SHOWING 1-10 OF 17 REFERENCES

### First-order definability of rational transductions: An algebraic approach

• Computer Science
2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
• 2016
It is shown that the FO-definability of a rational transduction is decidable, where FO- definable means definable in a first-order restriction of logical transducers à la Courcelle.

### A Circuit Complexity Approach to Transductions

• Computer Science
MFCS
• 2015
This work proposes to study these interactions at a functional level, by investigating the deterministic rational transductions computable by constant-depth, polysize circuits by introducing a circuit framework of independent interest that allows variable output length.

### Some operations and transductions that preserve rationality

• Economics
Theoretical Computer Science
• 1983
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not, for teaching and research institutions in France or abroad, or from public or private research centers.

### Duality and Equational Theory of Regular Languages

• Computer Science
ICALP
• 2008
This paper presents a new result in the equational theory of regular languages, which emerged from lively discussions between the authors about Stone and Priestley duality, and shows for instance that any class ofregular languages defined by a fragment of logic closed under conjunctions and disjunctions admits an equational description.

### Finite Automata, Formal Logic, and Circuit Complexity

This book discusses words and languages automata and regular languages semigroups and homomorphisms, formal languages and formal logic, regular languages and circuit complexity, and proof of the Krohn-Rhodes theorem proofs of the category theorems.

### On Profinite Uniform Structures Defined by Varieties of Finite Monoids

• Mathematics
Int. J. Algebra Comput.
• 2011
The notion of hereditary continuity is introduced and the behaviour of the three main properties (continuity, uniform continuity, hereditary continuity) under composition, product or exponential is discussed.

### Profinite Semigroups, Mal'cev Products, and Identities☆

• Mathematics
• 1996
Abstract We compute a set of identities defining the Mal'cev product of pseudovarieties of finite semigroups or finite ordered semigroups. We also characterize the pointlike subsets of a finite