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

By Bradley S. Tice

This paintings addresses the inspiration of compression ratios more than what has been identified for random sequential strings in binary and bigger radix-based structures as utilized to these usually present in Kolmogorov complexity. A fruits of the author’s decade-long learn that all started along with his discovery of a compressible random sequential string, the e-book keeps a theoretical-statistical point of advent compatible for mathematical physicists. It discusses the applying of ternary-, quaternary-, and quinary-based structures in statistical communique thought, computing, and physics.

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When a program is introduced to both random and non-random radix 5 based sequential strings that notes each similar subgroup of the sequential string as being a multiple of that specific character and affords a memory to that unit of information during compression, a sub-maximal measure of Kolmogorov Complexity results in the random radix 5 based sequential string. This differs from conventional knowledge of the random binary sequential string compression values. 75Kd 52 A Level of Martin-Lof Randomness Traditional literature regarding compression values of a random binary sequential string have an equal measure to length that is not reducible from the original state [1].

Jour. 27, 379–423 and 623–656 (1948). , Aspects of Kolmogorov Complexity: The Physics of Information. (River Publishers, Denmark, 2009). [6] Kotz, S. , Encyclopedia of Statistical Sciences (John Wiley & Sons, New York, 1982). Appendix B Random and Non-random Sequential Strings Using a Radix 5 Base System Bradley S. Tice Kolmogorov Complexity defi nes a random binary sequential string as being less patterned than a non-random binary sequential string. Accordingly, the non-random binary sequential string will retain the information about it’s original length when compressed, where as the random binary sequential string will not retain such information.

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].

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