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

By Bradley S. Tice

This paintings addresses the suggestion of compression ratios more than what has been recognized for random sequential strings in binary and bigger radix-based platforms as utilized to these generally present in Kolmogorov complexity. A fruits of the author’s decade-long study that started together with his discovery of a compressible random sequential string, the booklet keeps a theoretical-statistical point of advent appropriate for mathematical physicists. It discusses the appliance of ternary-, quaternary-, and quinary-based structures in statistical conversation idea, computing, and physics.

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J. Chaitin, Jour. ACM 16, 145–159 (1969). , Bell Labs. Tech. Jour. 27, 379–423 and 623–656 (1948). S. “The use of a radix 5 base for transmission and storage of information”, Poster for the Photonics West Conference, San Jose, California Wednesday January 23, 2008. [6] Kotz, S. I. 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.

But if the measure of the number and order of digits in a binary sequence of strings is the sole factor for defining a random or non-random trait to a binary sequential string, then it is possible to ‘reduce’ a random binary sequential string by some measure of itself in the form of sub-groups. These sub-groups, while not being as uniform as a non-random sub-group of a binary sequential string, will nonetheless compress from the original state to one that has reduced the redundancy in the string by implementing a compression in each sub-group of the random binary sequential string.

As an example the random binary sequential string [110001001101111] can be grouped into sub-groups as follows: {11}, {000}, {1}, {00}, {11}, {0}, and {111} with each sub-group bracketed into common families of like digits. An expedient method to reduce this string would be to take similar types and reduce to a single character that represented a multiple of the exact number of characters found in that sub-group. In this case taking the bracketed {11} and assign a multiple of 2 to a single character, 1, and then reduced it to a single character in the bracket that is underlined to note the placement of the compression.

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