Abstract
We consider circuits of functional elements of a finite depth whose elements are arbitrary Boolean functions of any number of arguments. We suggest a method of finding nonlinear lower bounds for complexity applicable, in particular, to the operator of cyclic convolution. The obtained lower bounds for the circuits of depth d ≥ 2 are of the form Ω(nλ d–1(n)). In particular, for d = 2, 3, 4 they are of the form Ω(n 3/2), Ω(n log n), and Ω(n log log n) respectively; for d ≥ 5 the function λ d–1(n) is a slowly increasing function. These lower bounds are the greatest known ones for all even d and for d = 3. For d = 2, 3, these estimates have been obtained in earlier studies of the author.
Comments (0)