The Bottom-Up Position Tree Automaton, the Father Automaton and their Compact Versions

TL;DR

This paper introduces new bottom-up tree automaton constructions from regular tree expressions, enabling links with deterministic recognizers and transition factorization, contrasting with classical top-down methods.

Contribution

It presents novel bottom-up automaton constructions based on Gluskov's and Ilie-Yu's approaches, with transition factorization techniques for more efficient automata.

Findings

New bottom-up automaton constructions from regular expressions

Transition factorization improves automaton efficiency

Links established with deterministic recognizers

Abstract

The conversion of a given regular tree expression into a tree automaton has been widely studied. However, classical interpretations are based upon a Top-Down interpretation of tree automata. In this paper, we propose new constructions based on the Gluskov's one and on the one of Ilie and Yu one using a Bottom-Up interpretation. One of the main goals of this technique is to consider as a next step the links with deterministic recognizers, consideration that cannot be performed with classical Top-Down approaches. Furthermore, we exhibit a method to factorize transitions of tree automata and show that this technique is particularly interesting for these constructions, by considering natural factorizations due to the structure of regular expression.