Title :
Better bounds for threshold formulas
Author :
Radhakrishnan, Jaikumar
Author_Institution :
Dept. of Comput. Sci., Rutgers Univ., New Brunswick, NJ, USA
Abstract :
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⩽k⩽n2, 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
Keywords :
threshold logic; better bounds; computation; monotone formula; nearly optimal bounds; stronger monotone contact networks model; threshold formulas; threshold functions; Boolean functions; Circuits; Computational complexity; Computer networks; Computer science; Input variables; Sorting; Upper bound;
Conference_Titel :
Foundations of Computer Science, 1991. Proceedings., 32nd Annual Symposium on
Conference_Location :
San Juan
Print_ISBN :
0-8186-2445-0
DOI :
10.1109/SFCS.1991.185384
