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Unpredictability in Future Microprocessors
prostoalex writes "A Business Week article says increase in chip speeds and number of transistors on a single microprocessor leads to varying degrees of unpredictability, which used to be a no-no word in the microprocessor world. However, according to scientists from Georgia Tech's Center for Research in Embedded Systems & Technology, unpredictability becomes a great asset leading to energy conservation and increased computation speeds."
This article left me rather insatisfied, so I looked for a better one. I found it here, a collection of papers on the subject, with real-world results, it seems. The first article is a nice overview, and there's some pics of odd-looking silicon. They have funding from DARPA, interestingly enough.
Problem: find a number larger than the median
proposed solution: pick 1000 entires at random and retain the highest.
analysis: at first glance it might seem that the problem seems ill formed since the size of the array is not specified. But note that this is not a parametric problem. You are asked for the median, so the actual numerical values of the array irrelevant, only the rank order. Some wiseguys here have suggested returning the largest double precision number as a gaurenteed bound. While a wise ass answer it does raise a second interesting false lead. Even if the number were represented in infinite precision and this could be aribtrarily large or small the proposed solution does not care. Again this is because all that matters is the ranking of the numbers not their values.
COnsider the proposed solution. pick any cell at random and examine the number. if this number is returned there is a 50% chance it is equal to or greater than the median of the set. (if this is not obvious, dwell on the meaning of the word median: it means half the numbers are above/below that number.). So the chance it is below the median is 0.5. if you choose 1000 numbers the chance that all are below the median is 0.5^1000 which is roughly 1 part in a google.
So the author is right, this algorithm fails less often than the probability that there is a cosmic ray that corrupts the calculation or their is a power blackout in the middle of it or that you have a heart attack.