Reduced Complexity Verification of Almost-Infinite-Step Opacity in Stochastic Discrete-Event Systems*

The analysis of infinite-step opacity in the context of stochastic discrete-event systems has been investigated as almost-infinite-step opacity for quantitative purposes. In this paper, we revisit the verification problem for almost-infinite-step opacity by concentrating on reducing its computational complexity. One of the key steps in the verification of almost-infinite-step opacity is the recognition of the unsafe language for infinite-step opacity. Inspired by recently developed techniques in the literature, we present an improved methodology for the calculation of the unsafe language for infinite-step opacity, which further improves the complexity of the verification of almost-infinite-step opacity.