The Complexity of Monotone Boolean Functions

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Mathematics (HMC)

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We study the realization of monotone Boolean functions by networks. Our main result is a precise version of the following statement: the complexity of realizing a monotone Boolean function of n arguments is less by the factor (2/πn)1/2, whereπ is the circular ratio, than the complexity of realizing an arbitrary Boolean function of n arguments. The proof combines known results concerning monotone Boolean functions with new methods relating the computing abilities of networks and machines.

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© 1977 Springer-Verlag

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