Event Concealment and Concealability Enforcement in Discrete Event Systems Under Partial Observation

In this article, we investigate event concealment and concealability enforcement in discrete event systems modeled as nondeterministic finite automata under partial observation. Given a subset of secret events in a given system, concealability holds if the occurrences of all secret events remain hidden to a curious observer (an eavesdropper). When concealability of a system does not hold, we analyze how a defensive function, placed at the interface of the system with the eavesdropper, can be used to enforce concealability by manipulating the observations generated by the system using event deletions, insertions, or replacements. The defensive function is said to be C-enforcing if, following the occurrence of secret events and regardless of earlier and subsequent activity generated by the system, it can always deploy a strategy to manipulate observations and conceal the secret events perpetually. We propose a polynomial complexity construction for obtaining one necessary and one sufficient condition for C-enforceability.