Optimal constructions for active diagnosis

Diagnosis is the task of detecting fault occurrences in a partially observed system. Depending on the possible observations, a discrete-event system may be diagnosable or not. Active diagnosis aims at controlling the system to render it diagnosable. Past research has proposed solutions for this problem, but their complexity remains to be improved. Here, we solve the decision and synthesis problems for active diagnosability, proving that (1) our procedures are optimal with respect to computational complexity, and (2) the memory required for our diagnoser is minimal. We then study the delay between a fault occurrence and its detection by the diagnoser. We construct a memory-optimal diagnoser whose delay is at most twice the minimal delay, whereas the memory required to achieve optimal delay may be highly greater. We also provide a solution for parametrized active diagnosis, where we automatically construct the most permissive controller respecting a given delay.