定义任意机器人的克里克-富兰克林-沃森基因（等价于有限状态机），并定义附加到每个基因的香农遗传代码；同时定义任意正则极大前缀码的克罗恩-罗兹复杂度
Defining the Crick-Franklin-Watson genes of any robot (equals a finite state machine) and defining the Shannon genetic code attached to each gene. We also define the Krohn-Rhodes complexity of any regular maximal prefix code
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中文总结 AI 辅助
本文探讨数学三大支柱的关联，证明克罗恩-罗兹复杂度c可判定，揭示复杂度c基本引理与马尔可夫链相关理论及有限自动机基因的意外联系，还定义了机器人基因、香农遗传代码及正则极大前缀码的克罗恩-罗兹复杂度
中文摘要 AI 辅助
本文将探讨数学三大支柱之间的关系：Marcel-Paul Schützenberger等人在码与自动机领域的重要研究；Persi Diaconis等人关于有限半群上的随机游走的研究；以及Stuart Margolis、Anne Schilling与笔者所用的有限半群理论高级技巧，用于证明克罗恩-罗兹复杂度c是可判定的。复杂度c基本引理（有限半群间的满同态在子群上为单射时保持c）与马尔可夫链的过去耦合、Diaconis的强平稳时间，以及有限自动机的克里克-富兰克林-沃森基因（本文将对其进行定义）之间存在非常令人惊讶的联系
英文摘要
This paper will discuss the relationships among three pillars of mathematics: important research in codes and automata by Marcel-Paul Schutzenberger and others; random walks on finite semigroups by Persi Diaconis and others; and advanced techniques from finite semigroup theory used in proving Krohn-Rhodes complexity c is decidable by Stuart Margolis, Anne Schilling, and myself. Very surprising connections exist between the Fundamental Lemma of Complexity c (epimorphisms between finite semigroups that are one-to-one on subgroups preserve c) and coupling from the past in Markov chains, Diaconis' strong stationary time, and the Crick-Franklin-Watson genes of a finite automaton (which will be defined in the paper).
发表机构
- University of California, Berkeley（加州大学伯克利分校）
机构由 AI 辅助整理，请以论文原文为准。
