Measuring static complexity. (1992)

• Record Type: Journal Article
• Authors: Goertzel, Ben
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 15:Number 1(1992)
• Page Start: 161
• Page End: 174
• Publication Date: 1992
• Subjects: Kolmogorov complexity -- algorithmic information -- pattern -- sophistication -- structure -- depth; Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171292000188
• Languages: English
• ISSNs: 0161-1712

Abstract

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.