A Level of Martin-Lof Randomness

By Bradley S. Tice

© 2013 – CRC Press

130 pages | 4 Color Illus. | 1 B/W Illus.

Purchasing Options:
Hardback: 9781578087518
pub: 2012-10-09
US Dollars$87.95
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About the Book

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

Introduction

Definition of a Level of Martin-Lof Randomness

Compression

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

Conclusions

Summary

References

Notes

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

Index

About the Author

Bradley S. Tice is the CEO of Advanced Human Design in Cupertino, California.

Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General
SCI040000
SCIENCE / Mathematical Physics