Overview
In mathematics there are limits, speed limits of a sort, on how many computational steps are required to solve certain problems. The theory of computational complexity deals with such limits, in particular whether solving an n-dimensional version of a particular problem can be accomplished with, say, 2 n n steps or will inevitably require 2 steps. Such a bound, together with a physical limit on computational speed in a machine, could be used to establish a speed limit for a particular problem. But there is nothing in the theory of computational complexity which precludes the possibility of constructing analog devices that solve such problems faster. It is a general goal of neural network researchers to circumvent the inherent limits of serial computation. As an example of an n-dimensional problem, one might wish to order n distinct numbers between 0 and 1. One could simply write all n ways to list the numbers and test each list for the increasing property. There are much more efficient ways to solve this problem; in fact, the number of steps required by the best sorting algorithm applied to this problem is proportional to n In n .
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Details
- ISBN-13: 9781461278368
- ISBN-10: 1461278368
- Publisher: Birkhauser
- Publish Date: November 2011
- Dimensions: 9.21 x 6.14 x 0.38 inches
- Shipping Weight: 0.57 pounds
- Page Count: 180
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