This paper deals with the diagnosability of discrete event systems (DES) modeled by labeled Petri nets (LPNs). An additional parameter K ∈ N, which is the number of observable events after an unobservable fault to ensure diagnosability, is discussed. With the incremental search of K, we transform the diagnosability problem into a series of K-diagnosability problems. For bounded diagnosable systems, Kmin , the minimum value of K to ensure diagnosability, can be eventually found. The state space is generated on the fly, without investigation of unnecessary states. This is a notable advantage compared with some existing methods, since just a part of the state space can often be sufficient to assess diagnosability.