ON THE DEPTH OF COMBINATIONAL CIRCUITS REQUIRED TO COMPUTE SWITCHING FUNCTIONS.

The properties of the O(log n)-depth realizable set of functions is discussed. It is shown that the necessary and sufficient condition for a set of functions A to be O(log n)-depth realizable is that there exist a Boolean expression for any n-variable function in A such that its literal number is bounded by a certain polynomial of n. It is shown that the family of linear functions, family of symmetrical functions and the family of threshold functions are O(log n)-depth realizable. Then, as a special case of the set of functions, a sequence of functions is introduced wherein exactly one n-variable function is contained for any n. The sequence of functions is in one-to-one correspondence to the formal language on right brace 0, 1 left brace and it is shown that the sequence of functions corresponding to the regular set is O (log n)-depth realizable.