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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

  • John Rhodes
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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).

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Cite

BibTeXRIS
BibTeX
@misc{rhodes2026defining,
  title = {{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}},
  author = {John Rhodes},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.29094},
  eprint = {2608.29094},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29094},
}
RIS
TY  - UNPB
TI  - 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
AU  - John Rhodes
PY  - 2026
DA  - 2026/08/29
PB  - arXiv
DO  - 10.48550/arxiv.2608.29094
UR  - https://arxiv.org/abs/2608.29094
AB  - 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).
ER  -