Regular Tree Algebras

TL;DR

This paper introduces a unique class of algebras that recognize regular tree languages, establishes their algebraic properties, and provides a characterization of these algebras.

Contribution

It defines a new class of regular tree algebras, proves their uniqueness as recognizers, and develops their algebraic characterization.

Findings

The class forms a pseudo-variety.

Existence of syntactic algebras is proven.

Provides an algebraic characterization of the class.

Abstract

We introduce a class of algebras that can be used as recognisers for regular tree languages. We show that it is the only such class that forms a pseudo-variety and we prove the existence of syntactic algebras. Finally, we give a more algebraic characterisation of the algebras in our class.