The complexity of monotone boolean functions |
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Authors: | Nicholas Pippenger |
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Affiliation: | (1) Mathematical Sciences Department, IBM Thomas J. Watson Research Center, 10598 Yorktown Heights, New York, USA |
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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/ n)1/2, where 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. |
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