A Level of Martin-Lof Randomness
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This work addresses the notion of compression ratios greater than what has been known for random sequential strings in binary and larger radix-based systems as applied to those traditionally found in Kolmogorov complexity. A culmination of the author’s decade-long research that began with his discovery of a compressible random sequential string, the book maintains a theoretical-statistical level of introduction suitable for mathematical physicists. It discusses the application of ternary-, quaternary-, and quinary-based systems in statistical communication theory, computing, and physics.
Table of Contents
Definition of a Level of Martin-Lof Randomness
Radix Numbers: A Historical Overview
Binary: An Overview of the Radix 2 System
Ternary: An Overview of the Radix 3 System
Quaternary: An Overview of the Radix 4 System
Quinary: An Overview of the Radix 5 System
Larger Radix Numbers
Universal and Truncated Applications
Appendix A: Compression and Geometric Data
Appendix B: Random and Nonrandom Sequential Strings Using a Radix 5 Base System
Appendix C: Patterns within Patternless Sequences
Appendix D: A Radix 4 Base System for Use in Theoretical Genetics
Appendix E: A Compression Program for Chemical, Biological, and Nanotechnologies
Appendix F: Babbage, Enigmas and Captain Crunch: An Essay
Appendix G: Innovations and Mathematics
Appendix H: Raymond J. Solomonoff: An Obituary
Bradley S. Tice is the CEO of Advanced Human Design in Cupertino, California.