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 recognized for random sequential strings in binary and bigger radix-based platforms as utilized to these often present in Kolmogorov complexity. A fruits of the author’s decade-long examine that all started along with his discovery of a compressible random sequential string, the ebook keeps a theoretical-statistical point of creation compatible for mathematical physicists. It discusses the appliance of ternary-, quaternary-, and quinary-based structures in statistical communique idea, computing, and physics.

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Group B oooOOQQQQ11IIIII If a compression program were to be used on Group A and Group B that consisted of underlining the first individual character of a similar group of sequential characters, moving towards the right, on the string and multiplying it by a formalized system of arithmetic as found in a Key, see Key Code A and key Code B, with the compression of Group A and Group B as the final result. Key Code A (For Group A) o O Q 1 I = = = = = x x x x x 3 3 3 3 3 Group AoOQ1I Resulting in a 5 character length for Group A.

Encyclopedia of Statistical Sciences (John Wiley & Sons, New York, 1982). Appendix C Patterns Within Patternless Sequences* Bradley S. 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.

24 A Level of Martin-Lof Randomness Key Code D (For Group D) o O Q 1 I = = = = = x x x x x 1 4 2 4 4 Group D oOQ1I Resulting in a 5 character length for Group D. As a final example Group A is a non-random sequential string and Group E as a random sequential string using a radix 5 characters for a total of 15 character length. A non-random string of radix 5 based characters with a 15 character length (Group A). Group A oooOOOQQQ111III A random string of a radix 5 based characters with a total of 15 character length (Group E).

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