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Lower bounds for complexity of Boolean circuits of finite depth with arbitrary elements
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D. Yu. Cherukhin
Published/Copyright:
November 15, 2011
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(nλd–1(n)). In particular, for d = 2, 3, 4 they are of the form Ω(n3/2), Ω(n log n), and Ω(n log log n) respectively; for d ≥ 5 the function λd–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.
Received: 2008-01-21
Published Online: 2011-11-15
Published in Print: 2011-November
© de Gruyter 2011
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