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The Permanent Requires Large Uniform Threshold Circuits
 

Summary: The Permanent Requires Large Uniform
Threshold Circuits
Eric Allendery
Department of Computer Science
Rutgers University
P.O. Box 1179
Piscataway, NJ 08855-1179
allender@cs.rutgers.edu.
May 6, 1998
Abstract
We show that thepermanent cannot be computed by uniform constant-
depth threshold circuits of size Tn, for any function T such that for all
k, Tk
n = o2n. More generally, we show that any problem that is
hard for the complexity class C=P requires circuits of this size on the
uniform constant-depth threshold circuit model. In particular, this lower
bound applies to any problem that is hard for the complexity classes PP
or P.
This extends a recent result by Caussinus, McKenzie, Th erien, and
Vollmer CMTV96 , showing that there are problems in the counting hier-

  

Source: Allender, Eric - Department of Computer Science, Rutgers University

 

Collections: Computer Technologies and Information Sciences