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.
Abstract- The paper will introduce the ternary, or radix 3, based system for use as a fundamental standard beyond the traditional binary, or radix 2, based system in use today. A compression level is noted that is greater than the known Martin-Lof standard of randomness in both binary and ternary sequential strings.
Index Terms- Radix 2, Binary, Radix 3, Ternary, Information Theory, Compression Ratio
I. Introduction
A ternary, or radix 3, based system is defined as three separate characters, or symbols, that have no semantic meaning apart from not representing the other characters. This is the same notion Shannon gave to the binary based system used in his paper's on information theory upon it's publication in 1948 (Shannon, 1948). Richards has noted that the radix 3 based system as the most efficient base, more so than even the radix 2 or radix 4 based systems (Richards, 1955: 8-9). A compression level is noted in this paper that is greater than the known Martin-Lof standard of randomness in both binary and ternary sequential strings.
II. Randomness
The earliest definition for randomness in a string of ľs and 0's was defined by von Mises, but it was Martin-Lof ' s paper of 1966 that gave a measure to randomness by the patterlessness of a sequence of 1's and 0's in a string that could be used to define a random binary sequence in a string (Martin-Lof, 1966). This is the classical measure for Kolmogorov complexity, also known as Algorithmic Information Theory, of the randomness of a sequence found in a binary string (Kotz and Johnson, 1982: 39). Martin-Lof (1966) also defined a random binary sequential string as being unable to compress from its original state. Nonrandom binary sequential strings can compress to less than there original state (Martin-Lof, 1966).
* Paper accepted and prepared for poster session Wednesday September 3, 2008 for the Royal Statistical Society 2008 Conference in Nottingham, England, United Kingdom, September 1-5, 2008.
The author contact information: Advanced Human Design, P.O. Box 3868 Turlock, California 95381 U.S.A., e-mail: paulatice@bigvalley.net
III. Compression Program
The compression program to be used has been termed the Modified Symbolic Space Multiplier Program as it simply notes the first character in a line of characters in a binary sequence of a string and subgroups them into common or like groups of similar characters, all ľ s grouped with ľ s and all O' s grouped with O' s, in that string and is assigned a single character notation that represents the number found in that sub-group, so that it can be reduced, compressed, and decompressed, expanded, back to it's original length and form. An underlined 1 or 0 is usually used to note the notation symbol for the placement and character type in previous applications of this program. An italicized character will be used for this paper.
IV. Binary System
The binary system, also known as a radix 2 based system, is composed of two characters, usually a 0 and a 1, that have no semantic properties except not representing the other. Group A will represent a nonrandom sequential binary string and Group В will represent a random sequential binary string. Both Group A and Group В will be 15 characters in total length.
Group A: [000111000111000] (Nonrandom)
Group B: [001110110011100] (Random)
Utilizing the Modified Symbolic Space Multiplier Program to process like sequential characters, either 0's or l's, into sub-groups and note them with an italicized character specific to that stab-group and having it represent a specific multiple of that sub-group as found in a key, in this case Group A Key and Group В Key, as a compressed aspect to both Group A and Group В sequential binary strings.
Group A Key: All italicized characters will represent a multiple of 3.
Group В Key: The italicized character 0 will represent a multiple of 2 and the italicized character 1 will represent a multiple of 3.
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- Quote paper
- Professor Bradley Tice (Author), 2012, A Comparison of Compression Values of Binary and Ternary Based Systems, Munich, GRIN Verlag, https://www.hausarbeiten.de/document/199142
