# Compression and Geometric Data

Essay 2012 6 Seiten

## ABSTRACT

Kolmogorov Complexity defines a random binary sequential string as being less patterned than a non-random binary sequential string. Accordingly, the non-random binary sequential string will retain the information about it's original length when compressed, where as the random binary sequential string will not retain such information. In introducing a radix 2 based system to a sequential string of both random and non-random series of strings using a radix 2, or binary, based system. When a program is introduced to both random and non-random radix 2 based sequential strings that notes each similar subgroup of the sequential string as being a multiple of that specific character and affords a memory to that unit of information during compression, a sub-maximal measure of Kolmogorov Complexity results in the random radix 2 based sequential string. This differs from conventional knowledge of the random binary sequential string compression values.

PACS numbers: 89.70 Eg, 89.70 Hj, 89.75 Fb, 89.75 Kd Traditional literature regarding compression values of a random binary sequential string have an equal measure to length that is not reducible from the original state[1]. Kolmogorov complexity states that a random sequential string is less patterned than a non-random sequential string and that information about the original length of the non-random string will be retained after compression [2]. Kolmogorov complexity is the result of the development of Algorithmic Information Theory that was discovered in the mid-1960's [3]. Algorithmic Information Theory is a sub­group of Information Theory that was developed by Shannon in 1948 [4].

Recent work by the author has introduced a radix 2 based system, or a binary system, to both random and non-random sequential strings [5]. A patterned system of segments in a binary sequential string as represented by a series of l's and 0's is rather a question of perception of subgroups within the string, rather than an innate quality of the string itself. While Algorithmic Information Theory has given a definition of patterned verses patternless in sequential strings as a measure of random verses non-random traits, the existing standard for this measure for Kolmogorov Complexity has some limits that can be redefined to form a new sub-maximal measure of Kolomogorov Complexity in sequential binary strings [6]. Traditional literature has a non-random binary sequential string as being such:[111000111000111] resulting in total character length of 15 with groups of l's and 0's that are sub-grouped in units of threes. A random binary sequence of strings will look similar to this example: [110100111000010] resulting in a mixture of sub­ groups that seem 'less patterned' than the non-random sample previously given.

Compression is the quality of a string to reduce from it's original length to a compressed value that still has the property of 'decompressing' to it's original size without the lose of the information inherent in the original state before compression.

[...]

[1] S. Kotz and N.I. Johnson, Encyclopedia of Statistical Sciences (John Wiley & Sons, New York, 1982).

[2] abide.

[3] R.J. Solomonoff, Inf. & Cont. 7, 1-22 & 224-254 (1964), A.N. Kolmogorov, Pro. Inf. & Trans. 1, 1-7 (1965) and G.J. Chaitin, Jour. ACM 16, 145-159 (1969).

[4] C.E. Shannon, Bell Labs. Tech. Jour. 27, 379-423 and 623-656 (1948).

[5] B.S. Tice, Aspects of Kolmogorov Complexity: The Physics of Information. (River Publishers, Denmark, 2009).

[6] S. Kotz and N.I. Johnson, Encyclopedia of Statistical Sciences (John Wiley & Sons, New York, 1982).

## Details

Seiten
6
Jahr
2012
ISBN (eBook)
9783656334163
ISBN (Buch)
9783656645276
Dateigröße
3.6 MB
Sprache
Englisch
Katalognummer
v199139
Note
A [4.00]
Schlagworte
compression geometric data