Mantika, Gilbert Tieudjo, Daniel
Published in
Lobachevskii Journal of Mathematics

We prove some conditions on a given abstract group G, such that the group Autc(G^\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat G$$\end{document}) of the continuo...

Pin, Jean-Eric Silva, Pedro

Given a variety of finite monoids V, a subset of a monoid is a V-subset if its syntactic monoid belongs to V. A function between two monoids is V-preserving if it preserves V-subsets under preimages and it is hereditary V-preserving if it is W-preserving for every subvariety W of V. The aim of this paper is to study hereditary V-preserving function...

Pin, Jean-Eric

This survey paper presents the success story of the topological approach to automata theory. It is based on profinite topologies, which are built from finite topogical spaces. The survey includes several concrete applications to automata theory.

Gehrke, Mai Grigorieff, Serge Pin, Jean-Eric

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. Let us call lattice of languages a class of regular languages closed under finite intersection and finite union. The main results of this paper can be summarized in a nutshell a...

Pin, Jean-Eric Silva, Pedro

In this paper, we prove an extension of Mahler's theorem, a celebrated result of p-adic analysis. Mahler's original result states that a function from N to Z is uniformly continuous for the p-adic metric d_p if and only if it can be uniformly approximated by polynomial functions. We prove the same result for functions from A* to Z, where d_p is now...

Pin, Jean-Eric Silva, Pedro

This paper is a contribution to the mathematical foundations of the theory of automata. We give a topological characterization of the transductions ? from a monoid M into a monoid N, such that if R is a recognizable subset of N, ?^{-1}(R) is a recognizable subset of M. We impose two conditions on the monoids, which are fullfilled in all cases of pr...

Pin, Jean-Eric

This main result of this paper states that a recognizable language is open in the Hall topology if and only if it belongs to the polynomial closure C of the group languages. A group language is a recognizable language accepted by a permutation automaton. The polynomial closure of a class of languages L is the set of languages that are finite unions...

Pin, Jean-Eric

This is a survey article on the combinatorial aspects of the p-adic metric and p-adic topology on words. We give several equivalent definitions of these notions, illustrated by several examples and properties. After giving a detailed description of the open sets, we prove that the p-adic metric is uniformly equivalent with a metric based on the bin...

Pin, Jean-Eric

A reversible automaton is a finite (possibly incomplete) automaton in which each letter induces a partial one-to-one map from the set of states into itself. We give four non-trivial characterizations of the languages accepted by a reversible automaton equipped with a set of initial and final states and we show that one can effectively decide whethe...