Comparing Labelled Markov Decision Processes

TL;DR

This paper develops polynomial-time algorithms to compare labelled Markov decision processes, focusing on strategy existence for equivalence or inequivalence, with implications for verification and anonymity.

Contribution

It introduces the first polynomial-time algorithms for strategy synthesis to establish inequivalence between labelled MDPs.

Findings

Polynomial-time algorithms for inequivalence strategies

Complexity results for probabilistic distance problems

Applications in verification and anonymity

Abstract

A labelled Markov decision process is a labelled Markov chain with nondeterminism, i.e., together with a strategy a labelled MDP induces a labelled Markov chain. The model is related to interval Markov chains. Motivated by applications of equivalence checking for the verification of anonymity, we study the algorithmic comparison of two labelled MDPs, in particular, whether there exist strategies such that the MDPs become equivalent/inequivalent, both in terms of trace equivalence and in terms of probabilistic bisimilarity. We provide the first polynomial-time algorithms for computing memoryless strategies to make the two labelled MDPs inequivalent if such strategies exist. We also study the computational complexity of qualitative problems about making the total variation distance and the probabilistic bisimilarity distance less than one or equal to one.