A mathematical concept is identified and analyzed that is implicit in the 2012 paper Turing Incomputable Computation, presented at the Alan Turing Centenary Conference (Turing 100, Manchester). The concept, called dynamic level sets, is distinct from mathematical concepts in the standard literature on dynamical systems, topology, and computability theory. A new mathematical object is explained and why it may have escaped prior characterizations, including the classical result of de Leeuw, Moore, Shannon, and Shapiro (1956) that probabilistic Turing machines compute no more than deterministic ones.

翻译：本文识别并分析了一个隐含于2012年阿兰·图灵百年纪念会议（图灵100，曼彻斯特）论文《图灵不可计算的计算》中的数学概念。该概念被称为动态层级集，区别于动力系统、拓扑学和可计算性理论标准文献中的数学概念。本文阐释了一种新的数学对象，并解释了为何该对象可能规避了先前的特征化描述，包括de Leeuw、Moore、Shannon和Shapiro（1956年）关于概率图灵机计算能力不超过确定性图灵机的经典结论。