Novel Lossless Compression Method Based on the Fourier Transform to Approximate the Kolmogorov Complexity of Elementary Cellular Automata
Novel Lossless Compression Method Based on the Fourier Transform to Approximate the Kolmogorov Complexity of Elementary Cellular Automata作者机构：Department of Computer Science University of York York UK
出 版 物：《Journal of Software Engineering and Applications》 (软件工程与应用（英文）)
年 卷 期：2022年第15卷第10期
页 面：359-383页
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
主 题：Fast Fourier Transform Lossless Compression Elementary Cellular Automata Algorithmic Information Theory Kolmogorov Complexity
摘 要：We propose a novel, lossless compression algorithm, based on the 2D Discrete Fast Fourier Transform, to approximate the Algorithmic (Kolmogorov) Complexity of Elementary Cellular Automata. Fast Fourier transforms are widely used in image compression but their lossy nature exclude them as viable candidates for Kolmogorov Complexity approximations. For the first time, we present a way to adapt fourier transforms for lossless image compression. The proposed method has a very strong Pearsons correlation to existing complexity metrics and we further establish its consistency as a complexity metric by confirming its measurements never exceed the complexity of nothingness and randomness (representing the lower and upper limits of complexity). Surprisingly, many of the other methods tested fail this simple sanity check. A final symmetry-based test also demonstrates our method’s superiority over existing lossless compression metrics. All complexity metrics tested, as well as the code used to generate and augment the original dataset, can be found in our github repository: ECA complexity metrics1.
维普期刊数据库