Download e-book for iPad: A Level of Martin-Lof Randomness by Bradley S. Tice

By Bradley S. Tice

ISBN-10: 1578087511

ISBN-13: 9781578087518

This paintings addresses the proposal of compression ratios more than what has been identified for random sequential strings in binary and bigger radix-based structures as utilized to these ordinarily present in Kolmogorov complexity. A end result of the author’s decade-long examine that all started together with his discovery of a compressible random sequential string, the ebook keeps a theoretical-statistical point of advent compatible for mathematical physicists. It discusses the appliance of ternary-, quaternary-, and quinary-based platforms in statistical conversation thought, computing, and physics.

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Extra resources for A Level of Martin-Lof Randomness

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N. Kolmogorov, Pro. Inf. & Trans. 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.

In other words, each sub-group of the random binary sequential string will compress, retain the memory of that pre-compression state, and then, When decompressed, produce the original number and order to random binary sequential string. The memory aspect to the random binary sequential string is, in effect, the retaining of the number and order of the information found in the original pre-compression state. This can be done by assigning a relation to the subgroup that has a quality of reducing and then returning to the original state Appendices 49 that can be done with the use of simple arithmetic.

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]. 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].

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


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