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Given a sequential switching function in the form of a flow table in which some of the entries are unspecified, the problem of reducing the number of rows in that flow table is extremely complex, and cannot, in general, be solved by any simple extension of the methods used for completely specified functions. An analysis of the problem is presented, and a partially enumerative solution is evolved. A rough indication of the efficiency of the given procedures may be obtained from the fact that these techniques have been successfully applied to approximately two dozen tables ranging up to about 15 rows. No solution required more than two hours.