Construction of rational expression from tree automata using a generalization of Arden's Lemma

TL;DR

This paper extends Arden's Lemma to rational tree languages and introduces a method to construct rational tree expressions from finite tree automata, enhancing the theoretical tools for tree automata analysis.

Contribution

It generalizes Arden's Lemma to rational tree languages and provides a construction method for rational tree expressions from finite tree automata.

Findings

Generalization of Arden's Lemma to rational tree languages

Construction method for rational tree expressions from automata

Theoretical framework for analyzing tree automata

Abstract

Arden's Lemma is a classical result in language theory allowing the computation of a rational expression denoting the language recognized by a finite string automaton. In this paper we generalize this important lemma to the rational tree languages. Moreover, we propose also a construction of a rational tree expression which denotes the accepted tree language of a finite tree automaton.