AI 中文总结
该文发展柯尔莫哥洛夫算法复杂性理论，修改随机性定义满足守恒不等式，可定义单个无限序列中的互信息等概念，并将其应用于多领域，通过特定假设简化了相关理论。
AI 中文摘要
本文进一步发展了柯尔莫哥洛夫算法复杂性理论。修改了随机性的定义以满足强不变性性质（守恒不等式）。这使得能够在单个无限序列中定义诸如互信息等概念。考虑了在概率论、算法理论、直觉主义逻辑等多个领域的应用。通过假设这些理论所考虑的对象与任何由数学性质指定的序列相互独立（互信息小），这些理论得到了大幅简化。
英文摘要
The article develops further Kolmogorov's Algorithmic Complexity Theory. The definition of Randomness is modified to satisfy strong invariance properties (conservation inequalities). This allows definitions of concepts such as Mutual Information in individual infinite sequences. Applications to several areas, like Probability Theory, Theory of Algorithms, Intuitionistic Logic are considered. These theories are simplified substantially with the postulate that the objects they consider are independent of (have small mutual information with) any sequence specified by a mathematical property.
Comments15 pages
Journal refInformation and Control, 61(1):15-37, April 1984
