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Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles

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On Tuesday, April 10, 2012 1:43:45 PM UTC+1, James Dow Allen wrote:
> On Apr 10, 4:29 pm, LawCouns...@aol.com wrote:
> > THE COMPLETE SPECIFICATIONS :
> > =============================
> >
> > 1. generates a number eg 1,000 of such sequences ( each sequence composed of ternary symbols 'a' 'b' 'c' , when # of 'c' = # of 'b' + 2 Then sequence ENDS  & next sequences begins ) using a source producing symbol 'a' 25% of times symbol 'b' 25% of times symbol 'c' 50% of times ) .... call the total # of symbols in these 1,000 sequences N . NOTE : among these eg 1,000 sequences the # of 'a' is invariable near = the # of 'b'  & the # of 'c' is invariable near = 2 * the # of 'b'  THUS the probability model here is 25% : 25% : 50%
> 
> I'm not clear on what "invariable near =" means.  I think you specify
> that the trit is from a random memoryless source.  (Anyway, a
> different
> intepretation would have smallish effect.)

If source produces symbol 'a' 25% of times symbol 'b' 25% of times symbol 'c' 50% of times THEN after eg 1,000 symbols sequences generated ( total N # of symbols within these 1,000 sequences ) THEN  can with very high confidence level says the # of 'a' will be around N/4   the # of 'b' will be around N/4   the # of 'c' will be around N/2 

> 
> > 2. compresses these eg 1,000 generated sequences using your .exe , & must decode back to the same 1,000 sequences
> 
> Does the decompressor know, in advance, the exact number of bits in
> the
> sequence?  (Even if it does, the compression savings will be tiny,
> when
> amortized over 1000 strings.)

you can ALWAYS choose ONLY a particular fixed # of sequences eg 1,000 or 10,000 etc to compress , so decompressor knows in advance the EXACT # of sequences compressed ..... but may ONLY guess at the total # of bits quite accurate ( since this is not known in advance )  
> 
> > 3. IF you compressed file bitslength  =<  1.5 * N   - ( 0.08 * N )  THEN YOU WIN THE REWARDS !
> 
> Starting with a source of exactly 1.500 bits/token of info,
> we wait for the 1000th terminal, then compress it to
> 1.420 bits/token.  Right?  Good luck!  :-)
> 
> I'll leave my bet on Shannon, Kraft, and the pigeons.

SO WOULD I should these 1,000 sequences being 'random' structureless .... here the structure is within each sequence the # of 'c' is EXACT = the # of 'b' + 2

IN FACT ... all sequence MUST END with a 'c'  , immediate before this 'c'  ONLY an 'a' OR a 'c'  can occur [ NEVER  a 'b' ! ] .... if you look more careful, there are many more restrictions on possible permutations 'ordered'arrangements between the # of 'a's & 'b' & 'c' within a sequence , eg if there are 6 symbols in a sequence 1st 2 symbols cant be both 'a's    &  last 3 symbols cant be ALL 'b's  .... etc so forth .... IT IS THESE THAT MAY MAKE YOUR SOUGHT FOR 1.420bits/token p[ossible achievable ( ? )  


 
> 
> James Dow Allen

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Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles LawCounsels@aol.com - 2012-03-31 10:32 -0700
  Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles Thomas Richter <thor@math.tu-berlin.de> - 2012-04-03 11:32 +0200
    Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles James Dow Allen <jdallen2000@yahoo.com> - 2012-04-03 09:07 -0700
      Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles LawCounsels@aol.com - 2012-04-06 01:24 -0700
        Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles LawCounsels@aol.com - 2012-04-08 00:41 -0700
          Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles James Dow Allen <jdallen2000@yahoo.com> - 2012-04-08 04:25 -0700
            Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles lawcounsels@gmail.com - 2012-04-08 22:58 -0700
              Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles James Dow Allen <jdallen2000@yahoo.com> - 2012-04-09 04:19 -0700
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles biject <biject.bwts@gmail.com> - 2012-04-09 09:03 -0700
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles LawCounsels@aol.com - 2012-04-10 02:29 -0700
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles James Dow Allen <jdallen2000@yahoo.com> - 2012-04-10 05:43 -0700
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles lawcounsels@gmail.com - 2012-04-10 06:39 -0700
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles lawcounsels@gmail.com - 2012-04-10 06:51 -0700
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles lawcounsels@gmail.com - 2012-04-10 07:29 -0700
                I knew I was going to dislike New Google Groups! James Dow Allen <jdallen2000@yahoo.com> - 2012-04-10 09:03 -0700
                Re: I knew I was going to dislike New Google Groups! LawCounsels <lawcounsels@gmail.com> - 2012-04-10 09:56 -0700
                Re: I knew I was going to dislike New Google Groups! James Dow Allen <jdallen2000@yahoo.com> - 2012-04-10 10:34 -0700
                Re: I knew I was going to dislike New Google Groups! lawcounsels@gmail.com - 2012-04-10 10:54 -0700
                Re: I knew I was going to dislike New Google Groups! James Dow Allen <jdallen2000@yahoo.com> - 2012-04-11 13:16 -0700
                Re: I knew I was going to dislike New Google Groups! LawCounsels <lawcounsels@gmail.com> - 2012-04-12 03:10 -0700
                Re: I knew I was going to dislike New Google Groups! LawCounsels <lawcounsels@gmail.com> - 2012-04-12 03:57 -0700
                Re: I knew I was going to dislike New Google Groups! biject <biject.bwts@gmail.com> - 2012-04-12 08:38 -0700
                Re: I knew I was going to dislike New Google Groups! LawCounsels <lawcounsels@gmail.com> - 2012-04-13 02:34 -0700
                Re: I knew I was going to dislike New Google Groups! Fibonacci Code <anglikai@gmail.com> - 2012-04-30 07:36 -0700
                Re: I knew I was going to dislike New Google Groups! lawcounsels@gmail.com - 2012-04-30 08:34 -0700
                Re: I knew I was going to dislike New Google Groups! Thomas Richter <thor@math.tu-berlin.de> - 2012-04-30 18:53 +0200
                Re: I knew I was going to dislike New Google Groups! Fibonacci Code <anglikai@gmail.com> - 2012-04-30 09:58 -0700
                Re: I knew I was going to dislike New Google Groups! lawcounsels@gmail.com - 2012-04-30 10:18 -0700
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles LawCounsels@aol.com - 2012-04-10 05:58 -0700
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles biject <biject.bwts@gmail.com> - 2012-04-10 07:26 -0700
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles LawCounsels <lawcounsels@gmail.com> - 2012-04-10 08:10 -0700
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles biject <biject.bwts@gmail.com> - 2012-04-10 11:02 -0700
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles LawCounsels <lawcounsels@gmail.com> - 2012-04-11 02:43 -0700
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles Thomas Richter <thor@math.tu-berlin.de> - 2012-04-11 02:47 +0200
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles LawCounsels <lawcounsels@gmail.com> - 2012-04-11 02:56 -0700
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles Thomas Richter <thor@math.tu-berlin.de> - 2012-04-11 16:26 +0200
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles James Dow Allen <jdallen2000@yahoo.com> - 2012-04-11 07:36 -0700
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles LawCounsels@aol.com - 2012-04-11 10:29 -0700
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles Thomas Richter <thor@math.tu-berlin.de> - 2012-04-12 02:27 +0200
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles LawCounsels <lawcounsels@gmail.com> - 2012-04-12 03:08 -0700
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles LawCounsels <lawcounsels@gmail.com> - 2012-04-12 03:34 -0700
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles Thomas Richter <thor@math.tu-berlin.de> - 2012-04-13 13:48 +0200
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles James Dow Allen <jdallen2000@yahoo.com> - 2012-04-13 05:15 -0700
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles lawcounsels@gmail.com - 2012-04-13 06:57 -0700
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles lawcounsels@gmail.com - 2012-04-13 07:03 -0700
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles lawcounsels@gmail.com - 2012-04-13 06:52 -0700
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles Thomas Richter <thor@math.tu-berlin.de> - 2012-04-14 00:54 +0200
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles LawCounsels <lawcounsels@gmail.com> - 2012-04-16 02:48 -0700
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles Thomas Richter <thor@math.tu-berlin.de> - 2012-04-16 13:08 +0200
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles lawcounsels@gmail.com - 2012-04-16 04:40 -0700
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles James Dow Allen <jdallen2000@yahoo.com> - 2012-04-16 08:11 -0700
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles Thomas Richter <thor@math.tu-berlin.de> - 2012-04-16 19:31 +0200
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles James Dow Allen <jdallen2000@yahoo.com> - 2012-04-16 14:27 -0700
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles LawCounsels <lawcounsels@gmail.com> - 2012-04-24 03:46 -0700
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles Jim Leonard <mobygamer@gmail.com> - 2012-04-24 07:27 -0700
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles Fibonacci Code <anglikai@gmail.com> - 2012-04-28 09:55 -0700
                Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles LawCounsels <lawcounsels@gmail.com> - 2012-04-16 02:34 -0700
    Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles LawCounsels@aol.com - 2012-04-04 00:35 -0700
      Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles LawCounsels@aol.com - 2012-04-04 00:38 -0700
        Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles LawCounsels@aol.com - 2012-04-04 04:06 -0700
  Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles Ernst <Ernst_Berg@sbcglobal.net> - 2012-04-06 19:48 -0700
  Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles LawCounsels@aol.com - 2012-04-07 02:28 -0700
    Re: Mankind's centuries old Kraft's Inequality / Pigeonholes hurdles lawcounsels@gmail.com - 2012-04-07 03:22 -0700

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