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Tree algebra of sofic tree languages∗

Published online by Cambridge University Press:  11 August 2014

Nathalie Aubrun  and
Marie–Pierre Béal
Nathalie Aubrun
Affiliation:
LIP, UMR 5668, ENS de Lyon, CNRS, France.. nathalie.aubrun@ens-lyon.fr
Marie–Pierre Béal
Affiliation:
Université Paris-Est, Laboratoire d’informatique Gaspard-Monge, UMR 8049 CNRS, France.; beal@univ-mlv.fr

Abstract

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We consider the languages of finite trees called tree-shift languages which are factorial extensible tree languages. These languages are sets of factors of subshifts of infinite trees. We give effective syntactic characterizations of two classes of regular tree-shift languages: the finite type tree languages and the tree languages which are almost of finite type. Each class corresponds to a class of subshifts of trees which is invariant by conjugacy. For this goal, we define a tree algebra which is finer than the classical syntactic tree algebra based on contexts. This allows us to capture the notion of constant tree which is essential in the framework of tree-shift languages.

Keywords

Symbolic dynamicstree-shifttree automatatree algebra

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