The task of diagnosis consists in detecting, without ambiguity, occurrence of faults in a partially observed system. Depending on the degree of observability, a discrete event system may be diagnosable or not. Active diagnosis aims at controlling the system in order to make it diagnosable. Solutions have already been proposed for the active diagnosis problem, but their complexity remains to be improved. We solve here the active diagnosability decision problem and the active diagnoser synthesis problem, proving that (1) our procedures are optimal w.r.t. to computational complexity, and (2) the memory required for the active diagnoser produced by the synthesis is minimal. We then focus on the delay between the occurrence of a fault 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 for a diagnoser with optimal delay may be highly greater.