Get A Level of Martin-Lof Randomness PDF

By Bradley S. Tice

ISBN-10: 1578087511

ISBN-13: 9781578087518

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 usually present in Kolmogorov complexity. A end result of the author’s decade-long study that begun along with his discovery of a compressible random sequential string, the booklet continues a theoretical-statistical point of advent compatible for mathematical physicists. It discusses the applying of ternary-, quaternary-, and quinary-based structures in statistical conversation thought, computing, and physics.

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A non-random radix 5 base sequential string will have the same character types: [0, 1, 2, 3 & 4] but with a regular pattern of groupings such as [00112233440011223344] that has a total character length of 20 and if all two sequentially similar characters are compressed using all 5 character types the following will occur: [0123401234] resulting in a compressed non-random radix 5 base sequential string of 10. The paper has shown that a sub-maximal measure of Kolmogorov complexity exists that has implications to a new standard of the precise measure of 56 A Level of Martin-Lof Randomness randomness in both a radix 2 and a radix 5 based number systems.

Kolmogorov complexity states that a random sequential string is less patterned than a non-random sequential string and that information about the original length of the non-random string will be retained after compression [2]. Kolmogorov complexity is the result of the development of Algorithmic Information Theory that was discovered in the mid-1960’s [3]. Algorithmic Information Theory is a sub-group of Information Theory that was developed by Shannon in 1948 [4]. Recent work by the author has introduced a radix 5 based system, or a quinary system, to both random and non-random sequential strings [5].

The Conclusions 37 work found in this monograph has shown that the traditional notion of a random sequential string as being invalid and that the measures of randomness found in the work of the author to be more precise and specific as in defining the nature of a random sequential string. 12 Summary The text has presented a model of randomness that is lower than the traditional norms found to measure a level of Martin-Lof randomness in a sequential string. This marks a new standard for the measure of randomness in a sequential string.

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


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