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The general problem of the use of context in computer character recognition is briefly reviewed. For the special case where the context is generated by a two-state stationary Markov chain, upper bounds are obtained for the average error probability of an optimal recognition procedure, based on compound decision functions. These bounds are nonparametric and simple functions of the "differences" between: 1) the a priori and transition probabilities of the context, and 2) the distributions of the measurements used to identify the characters. Some justiflcations, applications to systems design, and illustrative examples are given. An improvement is also obtained on a previously derived upper bound for procedures using no context.