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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**Extra info for A Level of Martin-Lof Randomness**

**Example text**

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].