Approximate Abstractions of Markov Chains with Interval Decision Processes (Extended Version)

TL;DR

This paper presents a novel abstraction technique for large Markov chains using interval decision processes, which reduces state space while maintaining low bisimulation error and comparable computational complexity.

Contribution

It introduces a new abstraction method that constructs abstract points as functions of concrete states, improving bisimulation accuracy without increasing complexity.

Findings

Smaller one-step bisimulation error compared to standard abstractions

Method for probabilistic model checking with similar computational complexity

Effective reduction of state space in large Markov chains

Abstract

This work introduces a new abstraction technique for reducing the state space of large, discrete-time labelled Markov chains. The abstraction leverages the semantics of interval Markov decision processes and the existing notion of approximate probabilistic bisimulation. Whilst standard abstractions make use of abstract points that are taken from the state space of the concrete model and which serve as representatives for sets of concrete states, in this work the abstract structure is constructed considering abstract points that are not necessarily selected from the states of the concrete model, rather they are a function of these states. The resulting model presents a smaller one-step bisimulation error, when compared to a like-sized, standard Markov chain abstraction. We outline a method to perform probabilistic model checking, and show that the computational complexity of the new method is comparable to that of standard abstractions based on approximate probabilistic bisimulations.