# New PDF release: A Level of Martin-Lof Randomness

ISBN-10: 1578087511

ISBN-13: 9781578087518

This paintings addresses the concept of compression ratios more than what has been identified for random sequential strings in binary and bigger radix-based platforms as utilized to these commonly present in Kolmogorov complexity. A end result of the author’s decade-long study that begun together with his discovery of a compressible random sequential string, the booklet keeps a theoretical-statistical point of advent compatible for mathematical physicists. It discusses the applying of ternary-, quaternary-, and quinary-based structures in statistical communique conception, computing, and physics.

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Extra info for A Level of Martin-Lof Randomness

Sample text

Key Code A (For Group A) o O Q 1 I = = = = = x x x x x 3 3 3 3 3 Group A oOQ1I Resulting in a 5 character length for Group A. 24 A Level of Martin-Lof Randomness Key Code D (For Group D) o O Q 1 I = = = = = x x x x x 1 4 2 4 4 Group D oOQ1I Resulting in a 5 character length for Group D. As a final example Group A is a non-random sequential string and Group E as a random sequential string using a radix 5 characters for a total of 15 character length. A non-random string of radix 5 based characters with a 15 character length (Group A).

22 A Level of Martin-Lof Randomness These findings are similar to Tice (2003) and have applications to both Algorithmic Information Theory and Information Theory. Some other examples using Example A Radix 5 characters [oOQ1I] to test random and non-random sequential strings. The following is a non-random string of a radix 5 based characters with a total of 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 C).

Traditional literature has a non-random binary sequential string as being such: [111000111000111] resulting in total character length of 15 with groups of 1’s and 0’s that are sub-grouped in units of threes. A random binary sequence of strings will look similar to this example: [110100111000010] resulting in a mixture of sub-groups that seem ‘less patterned’ than the non-random sample previously given. Appendices 53 Compression is the quality of a string to reduce from it’s original length to a compressed value that still has the property of ‘decompressing’ to it’s original size without the loss of the information inherent in the original state before compression.