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A Level of Martin-Lof Randomness

By Bradley S. Tice

CRC Press – 2013 – 130 pages

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  • Add to CartHardback: $83.95
    978-1-57808-751-8
    October 9th 2012

Description

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.

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

Author Bio

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

Name: A Level of Martin-Lof Randomness (Hardback)CRC Press 
Description: By Bradley S. Tice. 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...
Categories: Statistical Computing, Computational Physics