On Aug 31, 2004, at 15:56, John Denker wrote:
4) Don't forget the _recursion_ argument. Take their favorite algorithm (call it XX). If their claims are correct, XX should be able to compress _anything_. That is, the output of XX should _always_ be at least one bit shorter than the input. Then the compound operation XX(XX(...)) should produce something two bits shorter than the original input. If you start with a N-bit message and apply the XX function N-1 times, you should be able to compress each and every message down to a single bit.
Plus a string of log(N) bits telling you how many times to apply the decompression function!
Uh-oh, now goes over the judge's head ...
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