Approximate Bisimulation Minimisation

TL;DR

This paper introduces polynomial-time algorithms for minimising labelled Markov chains using approximate bisimulation, effective even with uncertain or sampled transition probabilities, and demonstrates their practical effectiveness.

Contribution

It presents a novel notion of approximate bisimulation quotient and algorithms that efficiently handle perturbed or sampled transition data.

Findings

Algorithms successfully recover the bisimulation structure of original systems.

Effective in scenarios with uncertain or perturbed transition probabilities.

Experimental results validate the approach's practical utility.

Abstract

We propose polynomial-time algorithms to minimise labelled Markov chains whose transition probabilities are not known exactly, have been perturbed, or can only be obtained by sampling. Our algorithms are based on a new notion of an approximate bisimulation quotient, obtained by lumping together states that are exactly bisimilar in a slightly perturbed system. We present experiments that show that our algorithms are able to recover the structure of the bisimulation quotient of the unperturbed system.