A Level of Martin-Lof Randomness by Bradley S. Tice

By Bradley S. Tice

This paintings addresses the proposal of compression ratios more than what has been identified for random sequential strings in binary and bigger radix-based platforms as utilized to these normally present in Kolmogorov complexity. A end result of the author’s decade-long examine that started together with his discovery of a compressible random sequential string, the booklet continues a theoretical-statistical point of advent appropriate for mathematical physicists. It discusses the applying of ternary-, quaternary-, and quinary-based structures in statistical communique idea, computing, and physics.

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Example [C] will represent the non-random radix 10 character sequential string. Example [C]: [0000111122223333444455556666777788 889999] Example [D] will represent the random radix 10 character sequential string. Example [D]: [00111222233333444444555555566666666 777777777888899] The non-random radix 10 sequential string will use the following Key Code Guide: Key Code Guide 0 1 2 3 4 5 6 7 8 9 = = = = = = = = = = x x x x x x x x x x 4 4 4 4 4 4 4 4 4 4 Resulting in the following compressed state of Example [C]: Example [C]: [0123456789] 30 A Level of Martin-Lof Randomness The following Key Code Guide will be used for random radix 10 sequential string as found in Example [D].

A patterned system of segments in a binary sequential string as represented by a series of 1’s and 0’s is rather a question of perception of subgroups within the string, rather than an innate quality of the string itself. While Algorithmic Information Theory has given a definition of patterned verses patternless in sequential strings as a measure of random verses non-random traits, the existing standard for this measure for Kolmogorov Complexity has some limits that can be redefined to form a new sub-maximal measure of Kolmogorov Complexity in sequential binary strings [6].

Tice While Kolmogorov complexity, also known as Algorithmic Information Theory, defines a measure of randomness as being pattern-less in a sequence of a binary string, such rubrics come into question when sub-groupings are used as a measure of such patterns in a similar sequence of a binary string. This paper examines such sub-group patterns and finds questions raised about existing measures for a random binary string. 40Ua Qualities of randomness and non-randomness have their origins with the work of von Mises in the area of probability and statistics [1].

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