Opacity Verification for a Class of Modular Discrete Event Systems

The verification of opacity of discrete event systems (DESs) is subjected to the curse of dimensionality because this issue has been proven to be EXPSPACE-complete. Therefore, how to improve the efficiency of opacity verification in DESs is crucial. We discuss in this paper the verification of several classes of opacity in modular discrete event systems (modular DESs) formalized as Cartesian composition of deterministic finite state automata. We derive the sufficient and necessary conditions for these opacity notions in modular DESs. Many examples are also used to explain the results obtained in this article. These results greatly reduce the computational complexity of verifying the opacity for modular DESs.