On the Length of the Smallest Uniform Experiment which Distinguishes the Terminal States of a Machine

The problem considered here is to obtain estimates of the length of the smallest experiment (on a machine) which is independent of the unknown initial state and which allows us, by observing the outputs, to distinguish the terminal state. The estimates obtained depend, of course, on the assumptions placed on the machine. In general, the bounds derived are slightly less than n ~, where n is the number of distinguishable states in the machine. For no really general class of machines is a best bound known.