回顾来看，Hartmanis 和 Stearns 的研究似乎与我的工作最为接近。我建议读者在看我的论文之前先翻翻《Algebraic Structure Theory of Sequential Machines》（1966），以了解我对该课题进行处理的背景动机。那本教材中的划分对（partition pairs）概念与谢尔宾斯基拓扑斯（Sierpinski topos）中的满同态类（epimorphism classes）刚好吻合。所以基本上，……
Upon review, Hartmanis and Stearns appear to have come closest to my work. I would recommend readers take a look at Algebraic Structure Theory of Sequential Machines (1966) prior to my paper to get a background motivation for my treatment of the subject. The idea of partition pairs in that textbook coincides with epimorphism classes in the Sierpinski topos. So basically,…
The basic idea of an information flow was introduced by Hartmanis and Stearns in the algebraic structure theory of sequential machines. This is a beautiful and elegant formalism for describing how information flows in sequential machines. Now using new mathematics I have put this theory on its highest level of generality. But its not…
……具有极其惊人的商逻辑（logic of quotients）。已经证明，Sets^(->) 中的对偶商逻辑在直观上类似于 Hartmanis 和 Stearns 在《Algebraic Structure Theory of Sequential Machines》（1966）中的划分对构造。因此，拓扑斯 Sets^(->) 的强大能力足以涵盖他们构建计算结构理论的核心构件，也足以涵盖我的。所有这些都表明，Sets^(->) 本身……
…has an incredibly remarkable logic of quotients. It has been shown that the dual logic of quotients in Sets^(->) is intuitively similar to the partition pairs construction of Hartmanis and Stearns in Algebraic Structure Theory of Sequential Machines (1966). So the immense power of the topos Sets^(->) is enough to capture their central construction for creating a computational structure theory, and mine. All this demonstrates that Sets^(->) by itself…
很喜欢这篇自传。噪声和微分让我想起了 Hartmanis & Stearns 的《Algebraic Structure Theory of Sequential Machines》（1966），后者大致研究了关于自动机处于何种状态的认知是如何随着反复的状态转移而扩散的。
Love the autobio. Noise and the differential reminds me of Hartmanis & Stearns, Algebraic Structure Theory of Sequential Machines (1966), in that the latter roughly studied how our knowledge of what state an automaton is in diffuses over repeated transitions.
你可能会对这个感兴趣：Hartmanis & Stearns 的《Algebraic Structure Theory of Sequential Machines》（1966）。
You may be interested in: Hartmanis & Stearns, Algebraic Structure Theory of Sequential Machines (1966)
回顾来看，Hartmanis 和 Stearns 的研究似乎与我的工作最为接近。我建议读者在看我的论文之前先翻翻《Algebraic Structure Theory of Sequential Machines》（1966），以了解我对该课题进行处理的背景动机。那本教材中的划分对（partition pairs）概念与谢尔宾斯基拓扑斯（Sierpinski topos）中的满同态类（epimorphism classes）刚好吻合。所以基本上，……
Upon review, Hartmanis and Stearns appear to have come closest to my work. I would recommend readers take a look at Algebraic Structure Theory of Sequential Machines (1966) prior to my paper to get a background motivation for my treatment of the subject. The idea of partition pairs in that textbook coincides with epimorphism classes in the Sierpinski topos. So basically,…
信息流的基本概念是由 Hartmanis 和 Stearns 在时序机代数结构理论中引入的。这是一个用来描述信息如何在时序机中流动的美丽而优雅的形式化体系。现在借助新的数学工具，我已经把这个理论推到了最高的泛化层级。但它并不是……
The basic idea of an information flow was introduced by Hartmanis and Stearns in the algebraic structure theory of sequential machines. This is a beautiful and elegant formalism for describing how information flows in sequential machines. Now using new mathematics I have put this theory on its highest level of generality. But its not…
……具有极其惊人的商逻辑（logic of quotients）。已经证明，Sets^(->) 中的对偶商逻辑在直观上类似于 Hartmanis 和 Stearns 在《Algebraic Structure Theory of Sequential Machines》（1966）中的划分对构造。因此，拓扑斯 Sets^(->) 的强大能力足以涵盖他们构建计算结构理论的核心构件，也足以涵盖我的。所有这些都表明，Sets^(->) 本身……
…has an incredibly remarkable logic of quotients. It has been shown that the dual logic of quotients in Sets^(->) is intuitively similar to the partition pairs construction of Hartmanis and Stearns in Algebraic Structure Theory of Sequential Machines (1966). So the immense power of the topos Sets^(->) is enough to capture their central construction for creating a computational structure theory, and mine. All this demonstrates that Sets^(->) by itself…
很喜欢这篇自传。噪声和微分让我想起了 Hartmanis & Stearns 的《Algebraic Structure Theory of Sequential Machines》（1966），后者大致研究了关于自动机处于何种状态的认知是如何随着反复的状态转移而扩散的。
Love the autobio. Noise and the differential reminds me of Hartmanis & Stearns, Algebraic Structure Theory of Sequential Machines (1966), in that the latter roughly studied how our knowledge of what state an automaton is in diffuses over repeated transitions.