Determinisation and Unambiguisation of Polynomially-Ambiguous Rational Weighted Automata

TL;DR

This paper investigates the decidability and computational complexity of converting polynomially-ambiguous rational weighted automata into equivalent deterministic or unambiguous forms, establishing PSPACE bounds.

Contribution

It proves that the determinisation and unambiguisation problems for polynomially-ambiguous weighted automata are in PSPACE, providing complexity bounds for these problems.

Findings

Both problems are in PSPACE for polynomially-ambiguous automata.

Decidability of these problems was known, but complexity bounds were previously unknown.

The results extend understanding of automata determinisation over the rational field.

Abstract

We study the determinisation and unambiguisation problems of weighted automata over the rational field: Given a weighted automaton, can we determine whether there exists an equivalent deterministic, respectively unambiguous, weighted automaton? Recent results by Bell and Smertnig show that the problem is decidable, however they do not provide any complexity bounds. We show that both problems are in PSPACE for polynomially-ambiguous weighted automata.