Opacity Verification in Stochastic Discrete Event Systems Using Two-way Observers

The opacity of stochastic discrete event system is studied for stochastic system models. Firstly, the notions of stochastic infinite-step opacity and stochastic K-step opacity are formalized. By constructing a validator based on a two-way observer, a necessary and sufficient condition is obtained to verify the stochastic infinite-step opacity and stochastic K-step opacity of systems by using the validator of two-way observer. Finally, the verification algorithm for stochastic infinite-step opacity and stochastic K-step opacity based on two-way observer is proposed.