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In digital communications, the theory of optimum data detection requires precise knowledge of the bit transition time at the receiver before bit-by-bit detection can be implemented. This paper presents a method for the optimum design of discrete sequential algorithms for bit synchronization which may readily be implemented with digital hardware or with a digital computer. The method is based on Bayes estimation, opitmization theory for discrete systems, and discrete invariant imbedding. Results of two examples indicate the efficacy of the method.