Tree languages and branched groups

Tree algebras and varieties of tree languages

We consider several aspects of Wilke’s [T. Wilke, An algebraic characterization of frontier testable tree languages, Theoret. Comput. Sci. 154 (1996) 85–106] tree algebra formalism for representing binary labelled trees and compare it with approaches that represent trees as terms in the traditional way. A convergent term rewriting system yields normal form representations of binary trees and co...

Bronchology – A Well Branched Tree

Groups and NTS Languages

The context-free groups are known to be exactly the tinitely generated virtually free groups [ 19, 111. We give here a new combinatorial property which characterizes these groups: they are “locally primary.” A corollary of this property is that the cylinder generated by the group languages is included in the family of NTS languages. In particular, every context-free group language is NTS.

Asynchronously automatic languages and groups

Let A be a finite alphabet and let L ⊂ (A∗)n be an n-variable language over A. We say that L is regular if it is the language accepted by a synchronous n-tape finite state automaton, it is quasi-regular if it is accepted by an asynchronous n-tape automaton, and it is weakly regular if it is accepted by a non-deterministic asynchronous n-tape automaton. We investigate the closure properties of t...

Formal languages and infinite groups

This article is an introduction to formal languages from the point of view of combinatorial group theory.