Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!mnetor!seismo!uwvax!uwmacc!uwmcsd1!uwm-cs!litow 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). ?