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Possibility for infinite compression
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mangodrunk
Aug 27, 2007, 10:19:30 PM8/27/07
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I'm wondering if it's possible to compress any file? Maybe a less
powerful theorem would be that if it's possible to compress a file
that is compressible infinite times. Or is it possible to compress any
file an infinite amount of times. According to
http://marknelson.us/2006/06/20/million-digit-challenge/ he states
that it can't be done because that means if you use the output of the
compressor as the input you will compress the file down to one bit
after n iterations. But what if the compression was modeled by an
infinite series that has a limit of n. Then in theory it would be
possible to compress the file an infinite amount of times and each
iteration is slightly more compressed than the input.
powerful theorem would be that if it's possible to compress a file
that is compressible infinite times. Or is it possible to compress any
file an infinite amount of times. According to
http://marknelson.us/2006/06/20/million-digit-challenge/ he states
that it can't be done because that means if you use the output of the
compressor as the input you will compress the file down to one bit
after n iterations. But what if the compression was modeled by an
infinite series that has a limit of n. Then in theory it would be
possible to compress the file an infinite amount of times and each
iteration is slightly more compressed than the input.
Thomas Richter
Aug 28, 2007, 2:39:09 AM8/28/07
to
mangodrunk schrieb:
> I'm wondering if it's possible to compress any file?
> I'm wondering if it's possible to compress any file?
No. Check for the counting argument ("aka pigeonhole principle").
So long,
Thomas
mangodrunk
Aug 28, 2007, 9:07:24 AM8/28/07
to
Thanks Thomas, I guess I should have RTFM:
http://www.faqs.org/faqs/compression-faq/part1/section-8.html . I
didn't believe it were possible, but I just wanted a clearer
understanding of things.
w
Aug 30, 2007, 8:51:59 PM8/30/07
to
On Aug 28, 2:19 pm, mangodrunk <mangodr...@gmail.com> wrote:
> I'm wondering if it's possible to compress any file? Maybe a less
> powerful theorem would be that if it's possible to compress a file
> that is compressible infinite times. Or is it possible to compress any
> file an infinite amount of times. According tohttp://marknelson.us/2006/06/20/million-digit-challenge/he states> I'm wondering if it's possible to compress any file? Maybe a less
> powerful theorem would be that if it's possible to compress a file
> that is compressible infinite times. Or is it possible to compress any
> that it can't be done because that means if you use the output of the
> compressor as the input you will compress the file down to one bit
> after n iterations. But what if the compression was modeled by an
> infinite series that has a limit of n. Then in theory it would be
> possible to compress the file an infinite amount of times and each
> iteration is slightly more compressed than the input.
If you can compress three files down to 1 bit then how can you
decompress it back to three different files?
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