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Better bounds for threshold formulas

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1 Author(s)
Radhakrishnan, J. ; Dept. of Comput. Sci., Rutgers Univ., New Brunswick, NJ, USA

The computation of threshold functions using formulas over the basis {AND, OR, NOT} is considered. It is shown that every monotone formula that computes the threshold function Tkn/2⩽kn2, has size Ω(nk log (n/(k-1))). The same lower bound is shown to hold even in the stronger monotone contact networks model. Nearly optimal bounds on the size of ΣΠΣ formulas computing Tkn for small k are also shown

Published in:

Foundations of Computer Science, 1991. Proceedings., 32nd Annual Symposium on

Date of Conference:

1-4 Oct 1991