We consider Petri net models of discrete event systems with faulty behaviors which are triggered by the firing of failure transitions. We extend a necessary and sufficient, condition for diagnosability shown by Sampath et al. to unbounded Petri nets. But it is algorithmically impossible to check the condition in general. We introiduce methods for modification of coverability trees in order to detect failure transitions. By using such approximated sets, we propose two kinds of diagnosers called a difference marking wdiagncser and an w-refined diagncser. For o b servable places whose token numbers are replaced by w in the coverability trees, the former diagnoser calculates difference between token numbers before and after partially observed markings change, and detects failures. In the latter diagnoser, we refine the symbol w, and modify the coverability tree in order to distinguish markings reachable by normal behaviors from those reachable by faulty behaviors.

Recently, many model-based fault detection methods have been proposed in discrete event systems. In this paper, we consider discrete event systems modeled by finite state machines, and propose a design method of a diagnoser which detects failurers in the discrete event systems via state and event observations. This diagnoser can detect failures more precisely than that using event observation only. This diagnoser performs diagnostics using on-line observations of the system behavior. It is said that the systems diagnosable if the diagnoser detects any failure using finite numbers of observation data after it occurs. We consider a necessary and sufficient condition for systems to be diagnosable.