Title :
The power of negative thinking in constructing threshold circuits for addition
Author :
Hofmeister, Thomas
Author_Institution :
Dortmund Univ., Germany
Abstract :
It has recently been shown that it is possible to add two binary numbers in threshold circuits of depth two with polynomial size. It is shown here that the most significant bit of addition, which is a monotone function, needs exponential size when computed in monotone threshold circuits of depth two. In fact, it is shown that even o (n/log n) negations do not suffice for polynomial size. This is the first example of such a gap for this model
Keywords :
adders; computational complexity; threshold logic; addition; binary numbers; depth two threshold circuits; exponential size; monotone function; monotone threshold circuits; negative thinking; polynomial size; Arithmetic; Boolean functions; Circuits; Design methodology; Frequency selective surfaces; Mercury (metals); Neural networks; Polynomials; Upper bound;
Conference_Titel :
Structure in Complexity Theory Conference, 1992., Proceedings of the Seventh Annual
Conference_Location :
Boston, MA
Print_ISBN :
0-8186-2955-X
DOI :
10.1109/SCT.1992.215377
