Comparing the notions of opacity for discrete-event systems

Opacity is an information flow property characterizing whether a system reveals its secret to passive observer. Several notions of opacity have been introduced in the literature. We study language-based opacity, current-state initial-state initial-and-final-state K-step and infinite-step opacity. Comparing natural question that has investigated summarized by Wu Lafortune, who provided transformations among and, for prefix-closed languages, also between extend these results showing all discussed are transformable each other. Besides deeper insight into differences notions, applications complexity results. In particular, computable polynomial time preserve number observable events determinism, hence computational complexities verification coincide. provide complete improved picture improve algorithmic deciding