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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Additional info for A Level of Martin-Lof Randomness
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]:  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 .
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 .