By Bradley S. Tice
This paintings addresses the idea of compression ratios more than what has been recognized for random sequential strings in binary and bigger radix-based structures as utilized to these routinely present in Kolmogorov complexity. A fruits of the author’s decade-long examine that started along with his discovery of a compressible random sequential string, the publication continues a theoretical-statistical point of advent appropriate for mathematical physicists. It discusses the appliance of ternary-, quaternary-, and quinary-based platforms in statistical communique concept, computing, and physics.
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Additional resources for A Level of Martin-Lof Randomness
6] Kotz, S. , Encyclopedia of Statistical Sciences (John Wiley & Sons, New York, 1982). Appendix B Random and Non-random Sequential Strings Using a Radix 5 Base System Bradley S. Tice Kolmogorov Complexity defi nes a random binary sequential string as being less patterned than a non-random binary sequential string. Accordingly, the non-random binary sequential string will retain the information about it’s original length when compressed, where as the random binary sequential string will not retain such information.
I have used the work of Richards (1955) and Knuth (1998) as a guide to the importance of these base numbering systems. Richards (1955) has noted that the radix’s 2, 3, 8, 10, 12, and 16 are the only radix numbers to be considered for computing machinery (Richards, 1955: 5). I will use the radix 8, radix 10, radix 12 and radix 16 for character types in this section keeping with the historical nature of use of these radix systems in mechanical instrumentation and calculating machines. Larger Radix Numbers 27 The Radix 8 Base Number System Knuth cites Charles XII of Sweden as to consider the use of the radix 8 system for calculations in 1717, but died in a battle before decreeing such a system (Knuth, 1998: 200).
Kolmogorov complexity is the result of the development of Algorithmic Information Theory that was discovered in the mid-1960’s . Algorithmic Information Theory is a sub-group of Information Theory that was developed by Shannon in 1948 . Recent work by the author has introduced a radix 2 based system, or a binary system, to both random and non-random sequential strings . A patterned system of segments in a binary sequential string as represented by a series of 1’s and 0’s is rather a question of perception of subgroups within the string, rather than an innate quality of the string itself.