The use of algorithmic complexity in compressing a random binary sequential string is used to redefine a measure of 'randomness' found using both Minimum Description Length, MDL, and Minimum Message Length, MML, that changes the very nature of thier measures of a binary sequential string. The 'compressible' random binary sequential string was discovered in 1998 by the author and this is the first application to both MDL and MML.
Table of Contents
1. Introduction
2. Minimum Message Length
3. Minimum Description Length
4. The Grammar of Form
5. A Compression Engine
6. A New Paradigm
7. Conclusion
8. Summary
9. Notes
10. References
11. About the Author
Research Objectives and Topics
This monograph investigates the compressibility of binary sequential strings by comparing traditional random models with a novel "summing engine" algorithm. It aims to demonstrate how this new approach triggers a paradigm shift in the fundamental understanding of both Minimum Message Length (MML) and Minimum Description Length (MDL) models within statistical physics.
- Analysis of traditional random binary strings versus "summing engine" strings.
- Evaluation of MML and MDL models as systems for measuring data compression.
- Examination of Kolmogorov Complexity in the context of binary sequential data.
- Development of a new paradigm for "a priori" and "a posteriori" algorithmic models.
Excerpt from the Book
A New Paradigm
If a ‘summing engine’ is used on a binary sequential string the following three results will occur: The pattern of the binary sequential string will be of a regular pattern or non-random distribution. The pattern of the binary sequential string will be of a non-regular pattern or of a random distribution. The pattern of the binary sequential string will be of both a regular and a random distribution.
Along with the three types of binary sequential string types, the fundamental properties of ‘a priori’ and ‘a posteriori’ mark the pre-algorithm and the post-algorithm models. A traditionally compressed binary sequential string would be non-random as follows: [1010101010]. A traditional binary sequential string would not compress as follows: [0111100011].
If a ‘summing engine’ is used as the algorithm both non-random and random binary sequential strings would both compress as follows: Non-random compression: [1010101010]. Compressed: [10] five times. Random compression: [1000110000] with [1x1] [0x3] [1x2] [0x4] or [1010].
Chapter Summaries
Introduction: Outlines the scope of the monograph, which focuses on the compressibility of binary strings using MML and MDL models.
Minimum Message Length: Explores the origins of MML as a fully subjective Bayesian model developed by Wallace and Boulton.
Minimum Description Length: Details Rissanen's MDL approach and its reliance on balancing data regularity to achieve compression.
The Grammar of Form: Discusses Martin-Lof’s algorithmic complexity and the distinction between regular and random patterns in binary strings.
A Compression Engine: Defines the "summing engine" algorithm as a systematic process for aggregating common binary characters.
A New Paradigm: Presents the impact of the "summing engine" on binary string compression and introduces a new conceptual framework.
Conclusion: Summarizes how the "summing engine" challenges existing measures of randomness and adds to the study of algorithmic complexity.
Summary: Reiterates that this work provides the first account of fundamental changes to MML and MDL theory through "summing engine" application.
Notes: Provides historical context regarding the evolution of MML and MDL theory.
References: Lists the academic literature and foundational works supporting the monograph.
About the Author: Provides a brief professional biography of Dr. Bradley S. Tice.
Keywords
Statistical Physics, Minimum Description Length, Minimum Message Length, Compression Engine, Binary Sequential String, Algorithmic Complexity, Kolmogorov Complexity, Bayesian Model, Data Compression, Randomness, Regularity, A Priori, A Posteriori, Information Theory, Binary Data.
Frequently Asked Questions
What is the primary subject of this monograph?
The monograph explores the compressibility of binary sequential strings and how a new algorithm, the "summing engine," alters current theoretical models.
What are the central topics covered?
The work focuses on Minimum Message Length (MML), Minimum Description Length (MDL), Kolmogorov Complexity, and the statistical properties of binary data.
What is the author's primary research goal?
The goal is to demonstrate a paradigm shift in how MML and MDL systems evaluate data compression by introducing the "summing engine."
Which scientific methodology is employed?
The author uses a comparative analytical methodology, evaluating traditional random models against the "summing engine" process to test for algorithmic regularity.
What does the main body of the work address?
The main body systematically defines the existing compression models, introduces the "summing engine," and examines its performance on both random and non-random binary sequences.
What are the key terms associated with this research?
Key terms include Kolmogorov Complexity, binary sequential strings, data compression, and Bayesian frameworks.
How does the "summing engine" differ from traditional compression?
Unlike traditional models that struggle with specific types of randomness, the "summing engine" is capable of compressing random binary sequences by aggregating liked-natured characters.
Why does the author consider this a paradigm shift?
Because the "summing engine" enables compression in scenarios previously defined as random, it necessitates a fundamental re-evaluation of the parameters used in MDL and MML models.
- Arbeit zitieren
- Professor Bradley Tice (Autor:in), 2012, Statistical Physics and the Fundamentals of Minimum Description Length and Minimum Message Length, München, GRIN Verlag, https://www.hausarbeiten.de/document/205420
