Failure diagnosis in large and complex systems is a critical task. In the realm of discrete event systems, Sampath et al. proposed a language based failure diagnosis approach. They introduced the diagnosability for discrete event systems and gave a method for testing the diagnosability by rst constructing a diagnoser for the system. The complexity of this method of testing diagnosability is exponential in the number of states of the system and doubly exponential in the number of failure types. In this paper, we give an algorithm for testing diagnosability that does not construct a diagnoser for the system, and its complexity is polynomial in the number of states of the system and exponential in the number of failure types
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