Problem
Research questions and friction points this paper is trying to address.
Crick-Franklin-Watson genes
Shannon genetic code
Krohn-Rhodes complexity
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
🤖 AI Summary
本文通过定义机器人基因、香农遗传密码及Krohn-Rhodes复杂度，探讨了编码、自动机理论与有限半群上的随机游走之间的关系。
📝 Abstract
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).
Innovation
Methods, ideas, or system contributions that make the work stand out.
Crick-Franklin-Watson genes
Krohn-Rhodes complexity
finite state machine
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