By Bradley S. Tice
This paintings addresses the concept of compression ratios more than what has been recognized for random sequential strings in binary and bigger radix-based structures as utilized to these normally present in Kolmogorov complexity. A end result of the author’s decade-long examine that begun along with his discovery of a compressible random sequential string, the publication keeps a theoretical-statistical point of creation compatible for mathematical physicists. It discusses the appliance of ternary-, quaternary-, and quinary-based structures in statistical communique idea, computing, and physics.
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Extra info for A Level of Martin-Lof Randomness
New York: chapman & Ha11/CRC. Notes Note #1 Charles Babbage designed, but did not construct, a calculating machine he called his ‘Analytical Engine’ in the early part of the 19th Century in England (Knuth, 1998: 201). Currently a United Kingdom campaign is underway to build a prototype of Charles Babbage’s Analytical Engine (Fildes, J. print=true, pp. 1–4). Note#2 The compression algorithm found in this monograph is the most precise and accurate level of randomness of a sequential string known in the field of statistics.
A non-random string of radix 5 characters with a 15 character length (Group A). Group A oooOOOQQQ111III A random string of a radix 5 based characters with a total of 15 character length (Group D). Group D oOOOOQQ1111IIII If a compression program were to be used on Group A and Group D that consisted of underlining the first individual character of a similar group of sequential characters, moving towards the right, on the string and multiplying it by a formalized system of arithmetic as found in a key, see Key Code A and Key Code D, with the compression of Group A and Group D as the final result.
The measure of the string’s randomness is just a measure of the patterned quality found in the string. The quality of ‘memory’ of the original precompressed state of the binary sequential string has to do with the quantity of the number of 1’s and 0’s in that string and the exact order of those digits in the original string are the measure of the ability to compress in the first place. Traditional literature has a non-random binary sequential string as being able to compress, while a random binary sequential string will not be able to compress.