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System-level diagnosis appears to be a viable alternative to circuit-level testing in complex multiprocessor systems. A completely new generalization of the characterization problem in the system-level diagnosis area is developed in this paper. This generalized characterization theorem provides necessary and sufficient conditions for any fault-pattern of any size to be uniquely diagnosable, under the symmetric, and asymmetric invalidation models with or without the intermittent faults. Moreover, it is also shown that the well known t-characterization theorems under these models can be derived as special cases. In addition to the generalization provided by these results, it is hoped that these results will also have a great impact on the diagnosis of faulty units in uniform structures based on the system-level diagnosis concepts and would be particularly useful in the diagnosis of WSI-oriented multiprocessor systems.