  This paper investigates the problem of co-synthesis of edit function and
supervisor for opacity enforcement in the supervisory control of discrete-event
systems (DES), assuming the presence of an external (passive) intruder, where
the following goals need to be achieved: 1) the external intruder should never
infer the system secret, i.e., the system is opaque, and never be sure about
the existence of the edit function, i.e., the edit function remains covert; 2)
the controlled plant behaviors should satisfy some safety and nonblockingness
requirements, in the presence of the edit function. We focus on the class of
edit functions that satisfy the following properties: 1) the observation
capability of the edit function in general can be different from those of the
supervisor and the intruder; 2) the edit function can implement insertion,
deletion, and replacement operations; 3) the edit function performs bounded
edit operations, i.e., the length of each string output of the edit function is
upper bounded by a given constant. We propose an approach to solve this
co-synthesis problem by modeling it as a distributed supervisor synthesis
problem in the Ramadge-Wonham supervisory control framework. By taking the
special structure of this distributed supervisor synthesis problem into
consideration and to improve the possibility of finding a non-empty distributed
supervisor, we propose two novel synthesis heuristics that incrementally
synthesize the supervisor and the edit function. The effectiveness of our
approach is illustrated on an example in the enforcement of the location
privacy.
