In the type of recognition system under discussion, the physical sample to be recognized is first subjected to a battery of tests; on the basis of the test results, the sample is then assigned to one of a number of prespecified categories. The theory of how test results should be combined to yield an optimal assignment has been discussed in an earlier paper. Here, attention is focused on the tests themselves. At present, we usually measure the effectiveness of a set of tests empirically, i.e., by determining the percentage of correct recognitions made by some recognition device which uses these tests. In this paper, we discuss some of the theoretical problems encountered in trying to determine a more formal measure of the effectiveness of a set of tests; a measure which might be a practical substitute for the empirical evaluation. Specifically, the following question is considered: What constitutes an effective set of tests, and how is this effectiveness dependent on the correlations among, and the properties of, the individual tests in the set? Specific suggestions are considered for the case in which the test results are normally distributed, but arbitrarily correlated. The discussion is supported by the results of experiments dealing with automatic recognition of hand-printed characters.

In the synthesis of switching circuits, a formal representation of the function to be realized by the circuit is first established and simplified as much as possible. Only then is construction of the circuit undertaken. It is argued that an analogous strategy should be followed in the synthesis of digital computer programs: the function to be realized by a program should first be established in a suitable formalism; the resulting formal expression should then be simplified as much as possible; only at this point should translation into the final ``machine'' program be undertaken. In the light of this discussion, the simplification of a certain type of elementary program, containing no branching or internal modification, is considered in detail. It is argued that the analysis of this type of program, whose formalization is called a ``computational chain,'' is a prerequisite to the analysis of more general programs. A system of notation is developed, and rules are given for minimizing the temporary storage requirements associated with a computational chain, for eliminating vacuous and redundant parts, and for forming combinations of chains.

According to the model discussed in this paper, a pattern recognizer is said to consist of two parts: a receptor, which generates a set of measurements of the physical sample to be recognized, and a categorizer, which assigns each set of measurements to one of a finite number of categories. The rule of operation of the categorizer is called the ``recognition function.'' The optimization of the recognition function is discussed, and the form of the optimal function is derived. In practice, a prohibitively large sample is required to provide a basis for estimating the optimal recognition function. If, however, certain assumptions about the probability distributions of the measurements are warranted, recognition functions that are asymptotically optimal may be obtained readily. A small numerical example, involving the recognition of the hand-printed characters A, B, and C is solved by means of the techiques described. The recognition accuracy is found to be 95 per cent.