Demuth的随机性之路
Demuth's path to randomness
摘要：
OsvaldDemuth（1936- 1988）从俄国构造数学学派的观点出发，研究了构造性分析。在他的工作过程中，他介绍了各种概念的有效零集，当措辞在古典语言，产生了一些重大的算法随机性的概念。此外，他证明了几个结果连接建设性的分析和随机性，只是后来重新发现。在本文中，我们跟踪的路径，采取Demuth从他的建构主义根源，他的建设性分析，算法的随机性和可计算性理论之间的相互作用的深入和创新的工作。我们将特别关注（i）Demuth的工作的可微性马尔可夫可计算函数和他的研究建设性版本的Denjoy替代，（ii）Demuth的独立发现的主要概念的算法随机性，以及发展Demuth随机性，和（iii）的相互作用的真值表reductionary，算法随机性，和semigenericity在Demuth的工作。
英文摘要：
Osvald Demuth (1936--1988) studied constructive analysis from the viewpoint of the Russian school of constructive mathematics. In the course of his work he introduced various notions of effective null set which, when phrased in classical language, yield a number of major algorithmic randomness notions. In addition, he proved several results connecting constructive analysis and randomness that were rediscovered only much later. In this paper, we trace the path that took Demuth from his constructivist roots to his deep and innovative work on the interactions between constructive analysis, algorithmic randomness, and computability theory. We will focus specifically on (i) Demuth's work on the differentiability of Markov computable functions and his study of constructive versions of the Denjoy alternative, (ii) Demuth's independent discovery of the main notions of algorithmic randomness, as well as the development of Demuth randomness, and (iii) the interactions of truth-table reducibility, algorithmic randomness, and semigenericity in Demuth's work.
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