Improving Stochastic Model Checking with Stochastic Bounds

Stochastic model checking requires the computation of steady-state or transient distribution for finite or infinite Markov chains for the evaluation of some formulas implying probabilities. However the numerical analysis of Markov chains is much less efficient than the sophisticated algorithmic techniques such as MTBDD developed for the deterministic model checking. We propose to simplify the numerical evaluation of probabilities using stochastic bounds. We show that this approach can be used to bound transient, steady-state and cumulative rewards and may help to evaluate efficiently formulas based on these rewards.