1st Edition

A Level of Martin-Lof Randomness

By Bradley S. Tice Copyright 2013
    130 Pages 4 Color & 1 B/W Illustrations
    by CRC Press

    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.

    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

    Biography

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