Characteristic measures of switching functions

Abstract A basic problem in switching theory is the optimal realizations of switching functions in a certain basis and with respect to a certain characteristic measure such as complexity, circuit cost, number of input terminals, delay time. Naturally this problem has received much attention and although a general solution has not been accomplished, many very good results have been obtained. This survey does not attempt to include all the literature concerning this general problem. Some outstanding and basic papers will be reviewed emphasizing ideas, assumptions, results and limitations. A measure of circuit performance, labeled L(n), a characteristic index of the class of n-variable functions, will be defined. This measure is an important tool for understanding the difficulties of the problem and for obtaining most of the results. This survey reviews the most significant literature on problems concerning characteristic measures of switching functions, and in particular, measures of circuit complexity, formula complexity or length, and delay time required to realize switching functions. The asymptotic and finite behavior, the upper and lower bounds, and the order of magnitude of L(n) are included for each particular case.

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