An approximation algorithm for labelled Markov processes: towards realistic approximation

Approximation techniques for labelled Markov processes on continuous state spaces were developed by Desharnais, Gupta, Jagadeesan and Panangaden. However, it has not been clear whether this scheme could be used in practice since it involves inverting a stochastic kernel. We describe a Monte Carlo based implementation scheme for this approximation algorithm. This is, to the best of our knowledge, the first implementation of this approximation scheme. The implementation involves some novel ideas about how to estimate infs using sampling and also replacing the explicit description of subsets of the state space by tests for membership. It is hoped that this work enables more applications of continuous probabilistic LMP theory to emerge.