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"Capacity of quasigroups for generating information" - invited talk at 2nd CiiT Conference of Informatics and Information Technology, Molika - Macedonia, December 2001 Capacity of quasigroups for generating information Danilo Gligoroski Institute of Informatics Faculty of Natural Sciences Skopje

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"Capacity of quasigroups for generating information" - invited talk at 2nd CiiT Conference of Informatics and Information Technology, Molika - Macedonia, December 2001 Transformation of strings Transformation of strings with 4x4 Qs –576 quasigroups –For every s {0,1,2,3} n n=1..6, there is at least one Q and k such that Q k (s)=00…0 –For n=7 there are 45 strings (0.27%) that CAN NOT be transformed in 00…0 –For n=8 there are 2,517 strings (3.84%) that CAN NOT be transformed in 00…0 –For n=9 there are 34,455 strings (13.14%) that CAN NOT be transformed in 00…0

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"Capacity of quasigroups for generating information" - invited talk at 2nd CiiT Conference of Informatics and Information Technology, Molika - Macedonia, December 2001 Transformation of strings with 5x5 Qs –161280 quasigroups –I have checked for every s {0,1,2,3,4} n, n=1..8,9,10,11, and 12, and ALWAYS there is at least one Q and k such that Q k (s)=00…0 – For n=10 there are 255,732 strings (24.39%) that CAN NOT be transformed in 00…0 – For n=11 there are 2,042,895 strings (48.71%) that CAN NOT be transformed in 00…0 – For n=12 there are 10,122,285 strings (60.33 %) that CAN NOT be transformed in 00…0 What is the capacity of the quasigroups of order 5, i.e. what is the smallest length of a string s {0,1,2,3,4} n that can not be transformed in 00..0 ?

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"Capacity of quasigroups for generating information" - invited talk at 2nd CiiT Conference of Informatics and Information Technology, Molika - Macedonia, December 2001 Hypothesis For every s {0,1,..255} n n 1000000 there is at least one Q (256x256) and k such that Q k (s)=00…0 Transformation of strings with 256x256 Qs –10 58000 quasigroups

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"Capacity of quasigroups for generating information" - invited talk at 2nd CiiT Conference of Informatics and Information Technology, Molika - Macedonia, December 2001 What is happening when you process a string 00…0 of length more then 200, with a quasigroup? Fractals & Symmetry Chaos

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"Capacity of quasigroups for generating information" - invited talk at 2nd CiiT Conference of Informatics and Information Technology, Molika - Macedonia, December 2001 Fractals & Symmetry Q 174 =

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"Capacity of quasigroups for generating information" - invited talk at 2nd CiiT Conference of Informatics and Information Technology, Molika - Macedonia, December 2001 Chaos Q 175 =

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"Capacity of quasigroups for generating information" - invited talk at 2nd CiiT Conference of Informatics and Information Technology, Molika - Macedonia, December 2001 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

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