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From: litow@uwm-cs.UUCP (Dr. B. Litow)
Newsgroups: sci.research
Subject: NC circuits
Message-ID: <484@uwm-cs.UUCP>
Date: Wed, 14-Jan-87 12:11:19 EST
Article-I.D.: uwm-cs.484
Posted: Wed Jan 14 12:11:19 1987
Date-Received: Thu, 15-Jan-87 00:39:24 EST
Distribution: na
Organization: U of Wi-Milw, College of Engineering
Lines: 14

I would like to suggest in a tentative way that A^(2/3) represents a kind
of physical upper bound on NC circuit size. NC is well represented by
planar technologies and A^(2/3) where A is Avogadro's Number gives,roughly,
the number of molecular dimension gates possible in a small 'plane' of
'ordinary' matter. This value is about 2^52.7 which accords nicely with
cubic and quartic degree circuit families. In the cubic case one gets data
size of 2^16 bits on input and for the quartic 2^12 bits. A good reference
to NC is "On Uniform Circuit Complexity" by W.Ruzzo,JCSS 1981,365-383.A
fairly recent look at NC is "A Taxonomy of Problems with Fast Parallel
Algorithms" in Inf. & Cont.,1985,2-22. 

Clearly this value A^(2/3) is very likely going to require a new method
of physically realizing boolean gates on the molecular level with dissipation
in the range < 100kT (anyway a few tens of eV). ?