Stability and Complexity of Minimising Probabilistic Automata

TL;DR

This paper presents a numerically stable polynomial-time algorithm for minimizing weighted automata with bounded error, and analyzes the complexity of probabilistic automata minimization, showing NP-hardness and PSPACE membership.

Contribution

It introduces a stable minimization algorithm for weighted automata and improves the complexity bounds for probabilistic automata minimization problems.

Findings

Polynomial-time, numerically stable minimization algorithm for weighted automata.

Proof that probabilistic automata minimization is NP-hard and in PSPACE.

Application of the algorithm to image compression.

Abstract

We consider the state-minimisation problem for weighted and probabilistic automata. We provide a numerically stable polynomial-time minimisation algorithm for weighted automata, with guaranteed bounds on the numerical error when run with floating-point arithmetic. Our algorithm can also be used for "lossy" minimisation with bounded error. We show an application in image compression. In the second part of the paper we study the complexity of the minimisation problem for probabilistic automata. We prove that the problem is NP-hard and in PSPACE, improving a recent EXPTIME-result.