Semi-groupes fortement automatiques

TL;DR

This paper introduces strongly automatic semigroups, a concept that extends automaticity, and provides a criterion for strong automaticity specifically for semigroups of eta-adic developments.

Contribution

The paper defines strongly automatic semigroups and establishes a criterion for their strong automaticity in the context of eta-adic semigroups.

Findings

Introduction of strongly automatic semigroups

Criterion for strong automaticity in eta-adic semigroups

Extension of automaticity concept

Abstract

In this paper, we introduce the notion of strongly automatic semigroup, which implies the usual notion of auto- maticity. We focus on semigroups of \beta-adics developpements, for which we obtain a criterion of strong automaticity.