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From: jqb@netcom.com (Jim Balter)
Subject: Re: Compression proof (was: e: rand() - implementation ideas [Q])
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References: <54lr8o$ndm@nntp.seflin.lib.fl.us> <jqbE0Dvyr.A9H@netcom.com> <327EF858.2B56@ix.netcom.com> <56ace5$th8@csugrad.cs.vt.edu>
Date: Tue, 12 Nov 1996 21:33:54 GMT
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In article <56ace5$th8@csugrad.cs.vt.edu>,
Jon A. Maxwell <jmaxwell@csugrad.cs.vt.edu> wrote:
>William Grosso wrote:
>] For it to be useful, it must also be 1 to 1 -- if T(w) = T(z)
>] for two distinct sequences w and z, then we wouldn't be able to
>] decompress.
>
>Why must the compression function be 1 to 1?
>
>If you have a method whereby you can tell which of many possible
>decompressions is correct then you could trade time for space, it
>seems to me.

Any decompression algorithm is precisely "a method whereby you can
tell which of many possible decompressions is correct".
Nothing was mentioned about time, so there is none to trade;
decompression algorithms can take as long (finitely) as you want.

>Or does the theory claim there isn't any method that would work
>for all data?

The proof is precisely of the fact that there isn't any algorithm that can
compress all data; no *net* gain is possible.
-- 
<J Q B>

