17- https://doi.org/10.1007/bf01768483
The complexity of monotone boolean functions
- Dec 1, 1977
- Mathematical Systems Theory
- Nicholas Pippenger
Abstract
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 ofn arguments is less by the factor (2/πn)1/2, whereπ is the circular ratio, than the complexity of realizing an arbitrary Boolean function ofn arguments. The proof combines known results concerning monotone Boolean functions with new methods relating the computing abilities of networks and machines.
- # Monotone Boolean Functions
- # Circular Ratio
- # Complexity Of Boolean Functions
- # Boolean Functions
- # Main Result
- # Arbitrary Function
- # Arbitrary Boolean Function
- # Function Ofn
- # Precise Version
