Categories of (ℓ, ℛ)-systems |
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Authors: | Michael Abib |
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Institution: | (1) Department of Electrical Engineering, Stanford University, Stanford, USA |
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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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