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

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 typically 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 creation appropriate for mathematical physicists. It discusses the appliance of ternary-, quaternary-, and quinary-based platforms in statistical verbal exchange idea, computing, and physics.

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I. (1982) Encyclopedia of Statistical Sciences. New York: John Wiley & Sons, Inc. A good source for encyclopedia level searches on statistics. Li, M. H. (1993/1997) An Introduction to Kolmogorov Complexity and its Applications. New York: Springer. The main source for information on Kolmogorov Complexity. Updated edition to be publishing in 2009. Martin-Lof, P. (1966) “The definition of random sequences”. Information and Control, Volume 9, pp. 602–619. Defining paper on a definition of a random sequence.

While most experts feel all random probabilities are by nature actually pseudo-random in nature, a sub-field of statistical communication theory, also known as information theory, has developed a standard measure of randomness known as Kolmogorov randomness, also known as Martin-Lof randomness, that was developed in the 1960’s [2,3 & 4]. This subfield of information theory is known as Algorithmic Information Theory [5]. What makes this measure of randomness, and non-randomness, so distinct is the *The paper was published by GRIN Publishing GmbH, Munich, Germany in 2012 58 A Level of Martin-Lof Randomness notion of patterns, and pattern less, sequences of 1’s and 0’s in a string of binary symbols [6].

11 Conclusions Traditional literature on algorithmic randomness has defined a random sequential string as being non-reducible, not compressible, and that only a non-random sequential string is compressible and de-compressible to its original state (See Note #2). This monograph has raised salient points in reconsidering the rather rigid definition of randomness to include those algorithmic systems that have random compressible sequential strings. Perhaps, as taking some of my ideas from my dissertation work on language and Godel’s theorem, the inclusion of the word ‘may’ be compressible, rather than the all pervasive ‘will’ be compressible to a random property to a definition of a random sequential string (Tice, 2008).

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