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Diagnosability of discrete event systems (DES) was formally defined in finite state machine (FSM) models by Sampath, et al. They gave a method for testing diagnosability by first constructing a diagnoser for the system. The complexity of this method is exponential in the number of states and doubly exponential in the number of failure types. Later, Yoo, et al. developed an algorithm to solve the diagnosability problem with polynomial complexity in the number of states. We explore diagnosability of discrete event systems modeled by Petri nets. This gives us an advantage to solve large real-world problems. First, diagnosability of Petri nets is defined in terms of net structures, then, we proposed an algorithm that could be used for checking diagnosability property of discrete event systems. Examples are given to illustrate the approach.