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The thing is, for any randomly generated program that computes pi correctly for some digits, that program can have add-on lines of code that don't essentially change it. It can have infinitely many add-ons. I don't see any way you could reasonably Pronounce a probalility measure on that space of unbounded finite randomly generated codes. I don't think the proper measure on such a space would even be a probability measure.
If this arguement really has technical merit, somebody has written a peer reviewed paper on it somewhere that you should be able to reference. I doubt you can do that.
PairTheBoard
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If you generate your input program by, say, flips of a fair coin, you are more likely to run into a relatively short self-delimiting program for output string S before you have huge add-ons that essentially do nothing and an enormously huge program for output string S. In fact, the probability that your machine outputs S is dominated by the probability for you to randomly generate the simplest few programs that compute S.
Much has been written about this stuff -- here's a nice little intro that I just googled:
http://www.research.ibm.com/journal/...ibmrd2104G.pdf
If you're only interested in the first peer-reviewed papers on the subject, look for the work of Solomonoff and Levin.