International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 1, Pages 161-174
doi:10.1155/S0161171292000188
Measuring static complexity
Department of Mathematics, University of Nevada, Las Vegas, Las Vegas 89154, NV, USA
Received 17 August 1990; Revised 1 March 1991
Copyright © 1992 Ben Goertzel. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The concept of “pattern” is introduced, formally defined, and used to analyze various measures of the complexity of finite binary sequences and other objects. The standard Kolmogoroff-Chaitin-Solomonoff complexity measure is considered, along with Bennett's ‘logical depth’, Koppel's ‘sophistication'’, and Chaitin's analysis of the complexity of geometric objects. The pattern-theoretic point of view illuminates the shortcomings of these measures and leads to specific improvements, it gives rise to two novel mathematical concepts--“orders” of complexity and “levels” of pattern, and it yields a new measure of complexity, the “structural complexity”, which measures the total amount of structure an entity possesses.