Hyper-Minimization for Deterministic Weighted Tree Automata

TL;DR

This paper introduces the first hyper-minimization algorithm for deterministic weighted tree automata over commutative semifields, achieving efficient state reduction with minimal semantic change.

Contribution

It extends hyper-minimization theory to weighted automata and provides an efficient algorithm with practical implementation insights.

Findings

Algorithm runs in O(m log n) time, matching unweighted case efficiency

First hyper-minimization method for weighted tree automata

Implementation remarks facilitate practical application

Abstract

Hyper-minimization is a state reduction technique that allows a finite change in the semantics. The theory for hyper-minimization of deterministic weighted tree automata is provided. The presence of weights slightly complicates the situation in comparison to the unweighted case. In addition, the first hyper-minimization algorithm for deterministic weighted tree automata, weighted over commutative semifields, is provided together with some implementation remarks that enable an efficient implementation. In fact, the same run-time O(m log n) as in the unweighted case is obtained, where m is the size of the deterministic weighted tree automaton and n is its number of states.