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Abstract—A variable-length distinguishing sequence (VLDS) is a preset distinguishing sequence X<L>0</L> such that, if the machine is started in an unknown state, the output response of the machine to some prefix of X<L>0</L> will identify the initial state. The length of the required prefix is a function of the initial state. The properties of such sequences are investigated and a method which employs a modified version of the diagnosing tree is developed for generating and displaying all such sequences. The fixed-length distinguishing sequence (FLDS) is shown to be a special case of the more general VLDS. The VLDS is next applied in the design of simple and efficient preset fault-detection experiments for sequential machines.