Capacity of quasigroups for generating information

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Capacity of quasigroups for generating information

• Danilo Gligoroski
• Institute of Informatics
• Faculty of Natural Sciences
• Skopje

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Transformation of strings

• Transformation of strings with 4x4 Qs
• 576 quasigroups
• For every s?0,1,2,3n n1..6, there is at least
  one Q and k?? such that Qk(s)000
• For n7 there are 45 strings (0.27) that CAN NOT
  be transformed in 000
• For n8 there are 2,517 strings (3.84) that CAN
  NOT be transformed in 000
• For n9 there are 34,455 strings (13.14) that
  CAN NOT be transformed in 000

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• For n10 there are 255,732 strings (24.39) that
  CAN NOT be transformed in 000
• For n11 there are 2,042,895 strings (48.71)
  that CAN NOT be transformed in 000
• For n12 there are 10,122,285 strings (60.33 )
  that CAN NOT be transformed in 000

• Transformation of strings with 5x5 Qs
• 161280 quasigroups
• I have checked for every s?0,1,2,3,4n,
  n1..8,9,10,11, and 12, and ALWAYS there is at
  least one Q and k?? such that Qk(s)000

• What is the capacity of the quasigroups of order
  5, i.e. what is the smallest length of a string
  s?0,1,2,3,4n that can not be transformed in
  00..0 ?

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Hypothesis

• Transformation of strings with 256x256 Qs
• 1058000 quasigroups

• For every s?0,1,..255n n?1000000 there is at
  least one Q (256x256) and k?? such that Qk(s)000

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What is happening when you process a string 000
of length more then 200, with a quasigroup?

• Fractals Symmetry
• Chaos

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Fractals Symmetry
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Chaos
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Related work

• A new kind of science Stephen Wolfram
• Algorithmic information - Chaitin
• Process Physics Modeling Reality as
  Self-Organising Information R.T.Cahill,
  M.Klinger, K.Kitto