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'Does this algorithm exist?'
2000\02\25@113712 by MegaBolt

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Oops, For files of K bits, those files that can be mapped to a smaller files
should be (1-2^(1-K))*2^K and the remaining files are 2^(1-K)*2^K.  Both
these number should sum to 2^K.

Change 2^K to K in the earlier posting.

This expression are evaluated from the series repeated here again

Number of files of size one bit less that K  =2^(K-1)=2^(-1)(2^K)
Number of files of size two bit less that K  =2^(K-2)=2^(-2)(2^K)

... and so on ....

Number of files of size 1 bit

The total number of files of size smaller than K bits is the sum of the
series times 2^K (ie. sum of a series times the sum of all K bits files)

(  2^(-1)+ 2^(-2)+............+2^(1-K) )  *  (2^K)

Sum of the series is 2^(-1)( 1 - 2^((-1)(K-1))   sum of a geometric series
                                  --------------------------------   of
common ratio 2^(-1)
                                     1 - 2^(-1)
which evalutes to 1-2^(1-K).  Which gives us the number of all files of size
smaller than K bits as (1-2^(1-K))*2^K.

As for mapping one K bits file to file of size ZERO bit; well, where are you
going to store this file?  And how are going to share with someone?

Dale King <> wrote in message
> Care to explain how you arrived at those formulas? They are obviously
> wrong because for instance as k gets larger you can compress all the
> files of k bits except for a miniscule fractional file that goes rapidly
> to zero as k gets larger (at k=5, Excel gives me 2^k).

2000\02\25@235533 by MegaBolt

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   The formulas reduces to (2^K) - 2.

If you accept the case of zero bit file, then when you send the compressor
the length of the file to be decompressed send, a indeterminate value.  On
resend, send again the indeterminate value to confirm.  Then have the
compressor map this to the last remaining file.  If "NOTHING" can be mapped
to a file, then "SOMETHING BROKEN" is over qualified to be mapped to a file.
It at least screams out its existences in a directory; a file not there is
simply not there.

Then, now this is serious, by mathematical induction we can then reduce all
compressed files of bigger size further to smaller files and eventually all
files are mapped to either zero bit or indeterminant bit size.

We didn't just bash a few theorems.

We've just collasped the universe to void by a series of mapping.  Given
"NOTHING" , and depending on which path (of mapping) taken, any  files can
be recovered.

Algorithmic compession!!!!!!  Which is something we all have at the back of
our mind isn't it.

Crazier everyday!

Dale King <> wrote in message
> And doing the math gives you (2^K)-2 for the first formula and 2 for the
> second one. The only difference then between our formulas is that you
> don't believe you can have a zero byte file.

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