Abstract
We show that when we represent (ℓ, ℛ)-systems with fixed genome as automata (sequential machines), we get automata with output-dependent states. This yields a short proof that ((ℓ, ℛ)-systems from a subcategory of automata—and with more homomorphisms than previously exhibited. We show how ((ℓ, ℛ)-systems with variable genetic structure may be represented as automata and use this embedding to set up a larger subcategory of the category of automata. An analogy with dynamical systems is briefly discussed. This paper presents a formal exploration and extension of some of the ideas presented by Rosen (Bull. Math. Biophyss,26, 103–111, 1964;28, 141–148;28 149–151). We refer the reader to these papers, and references cited therein, for a discussion of the relevance of this material to relational biology.
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Literature
Arbib, M. A. 1965. “A Common Framework for Automata Theory and Control Theory”.Siam J. on Control, Ser. A,3, 206–222.
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— 1966b. “A Note on Replication in ((ℓ, ℛ)-systems”,,28, 149–151.
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Abib, M. Categories of (ℓ, ℛ)-systems. Bulletin of Mathematical Biophysics 28, 511–517 (1966). https://doi.org/10.1007/BF02476858
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DOI: https://doi.org/10.1007/BF02476858