The paper will present a comparison of a Radix 2 based system and the Radix 3 based system using an algorithmic complexity program for compression of both random and non-random sequential strings. The results show greater compression in both the Radix 2 and the Radix 3 based number system in both random and non-random sequential strings.
Table of Contents
I. Introduction
II. Randomness
III. Compression Program
IV. Binary System
V. Ternary System
VI. Application of Theory
Research Objectives and Themes
The paper explores the implementation of ternary (radix 3) systems as a fundamental standard for data compression, comparing their efficiency against traditional binary (radix 2) systems and evaluating their performance in relation to existing standards of randomness.
- Comparison of binary and ternary data compression efficiency.
- Evaluation of algorithmic complexity and Martin-Lof randomness standards.
- Introduction of the Modified Symbolic Space Multiplier program for sequence reduction.
- Practical implications for telecommunications and computing infrastructures.
Excerpt from the Publication
V. Ternary System
A ternary, or radix 3, based system there are three characters used that have no semantic meaning except not representing the other two characters. Group C will represent a nonrandom ternary sequential string and Group D will represent a random ternary sequential string. The total length for each group, Group C and Group D, will be 12 characters in length. The three characters to be used in this study are a 0, 1, and 2.
Group C: [001122001122]
Group D: [001222011222]
Again each group will be assigned a specific compression multiple based on a specific character type, in this case an italicized 0, 1, and a 2, as defined in a key, Group C Key and Group D Key.
Group C Key: The italicized characters 0, 1 and 2 will represent each a multiple of 2.
Group D Key: The italicized character 0 will represent a multiple of 2. The italicized character 1 will represent a multiple of 2 and the italicized character 2 will represent a multiple of 3.
Group C: [012012]
Group D: [012012]
The compressed state of group C, nonrandom, is 6 characters in length. The compressed string of Group D, random, is 6 characters in length. Again note that Group D, the random sequential ternary string, is less than it's pre-compressed state, and again, is novel for those extrapolations of binary examples found in Kolmogorov Complexity.
Summary of Chapters
I. Introduction: Sets the stage by defining ternary systems as a potential alternative to the traditional binary standard in data processing.
II. Randomness: Reviews historical definitions of randomness, including the contributions of von Mises and Martin-Lof regarding sequence complexity.
III. Compression Program: Describes the technical methodology behind the Modified Symbolic Space Multiplier, which organizes characters into sub-groups for reduction.
IV. Binary System: Demonstrates the compression process using binary sequences and establishes the baseline performance for randomness evaluations.
V. Ternary System: Explores the application of compression multiples to ternary sequences and highlights the reduction efficiency compared to the original length.
VI. Application of Theory: Discusses the practical benefits of adopting ternary systems for future telecommunications and computing applications.
Keywords
Radix 2, Binary, Radix 3, Ternary, Information Theory, Compression Ratio, Kolmogorov Complexity, Modified Symbolic Space Multiplier, Data Transmission, Randomness, Sequential Strings, Telecommunications, Computing, Algorithms, Data Compression.
Frequently Asked Questions
What is the primary focus of this research?
The paper examines whether ternary (radix 3) systems can serve as a more efficient standard for data compression than current binary (radix 2) systems.
What are the main thematic fields discussed?
The research intersects information theory, computational data compression, and the mathematical definition of randomness.
What is the central research question?
The study asks if a ternary-based system can provide higher compression levels and greater robustness for information systems compared to existing binary standards.
Which methodology is employed in the study?
The author uses the "Modified Symbolic Space Multiplier" program to group sequential characters and test compression ratios on both random and non-random binary and ternary strings.
What topics are covered in the main body?
The main body covers the theoretical definitions of randomness, the practical application of the compression program, and side-by-side performance tests of binary vs. ternary sequences.
Which keywords define this paper?
Key terms include Radix 2, Radix 3, Compression Ratio, Information Theory, and Kolmogorov Complexity.
How is the Modified Symbolic Space Multiplier defined?
It is a program designed to identify commonalities in character strings to reduce them into a more compact, compressed form based on specific character keys.
What does the author conclude regarding ternary systems?
The author suggests that ternary systems provide more variety and potentially more robust communication architectures than current systems.
- Quote paper
- Professor Bradley Tice (Author), 2012, A Comparison of Compression Values of Binary and Ternary Based Systems, Munich, GRIN Verlag, https://www.grin.com/document/199142
