Compression of random binary data

[jonas.thornvall at gmail.com]

Den onsdag 13 juli 2016 kl. 00:24:23 UTC+2 skrev Ian:
> On Tue, Jul 12, 2016 at 11:35 AM,  <jonas.thornvall at gmail.com> wrote:
> >
> > No it is only compressible down to a limit given by the algorithm.
> 
> Then your algorithm does not compress random data as you claimed.
> 
> For some input, determine the limiting output that it ultimately
> compresses down to. Take that output and feed it through your
> algorithm as if it were the original input. If the data are to be
> considered random, then this input is just as probable as the
> original. What output does the algorithm now create? If it just
> returns the input unchanged, then how do you discern the original
> input from this input when decompressing? If it returns a different
> output of the same size, then repeat the process with the new output.
> Now there are *two* outputs of that size that can't be repeated. There
> are only finitely many possible outputs of that size, so eventually
> you're going to have to get to one that either repeats an output -- in
> which case your algorithm produces the same output for two different
> inputs and is therefore incorrect -- or you will get to an input that
> produces an output *larger* in size than the original.

The later sounds reasonable that is start toggle between states.