A decidable characterization of locally testable tree languages

TL;DR

This paper proves that it is decidable to determine whether a regular tree language is locally testable, applicable to both ranked and unranked unordered trees, advancing understanding of tree language properties.

Contribution

The paper establishes the first decidability result for checking local testability of regular tree languages in both ranked and unranked unordered trees.

Findings

Decidability of local testability for regular tree languages

Applicable to ranked and unranked unordered trees

Advances theoretical understanding of tree language properties

Abstract

A regular tree language L is locally testable if membership of a tree in L depends only on the presence or absence of some fix set of neighborhoods in the tree. In this paper we show that it is decidable whether a regular tree language is locally testable. The decidability is shown for ranked trees and for unranked unordered trees.