Article ID Journal Published Year Pages File Type
436383 Theoretical Computer Science 2008 24 Pages PDF
Abstract

The multiplicative complexity of a Boolean function f is defined as the minimum number of binary conjunction (AND) gates required to construct a circuit representing f, when only exclusive-or, conjunction and negation gates may be used. This article explores in detail the multiplicative complexity of symmetric Boolean functions. New techniques that allow such exploration are introduced. They are powerful enough to give exact multiplicative complexities for several classes of symmetric functions. In particular, the multiplicative complexity of computing the Hamming weight of n bits is shown to be exactly n−HN(n), where HN(n) is the Hamming weight of the binary representation of n. We also show a close relationship between the complexities of basic symmetric functions and the fractal known as Sierpinski’s gasket.

Related Topics
Physical Sciences and Engineering Computer Science Computational Theory and Mathematics