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Abstract biological systems as sequential machines

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Abstract

It is shown that a rather close relationship exists between the (ℳ,ℛ)-systems, defined previously as prototypes of abstract biological systems, and the sequential machines which have been studied by various authors. The theory of sequential machines is reformulated in a way suitable for its application to the study of the intertransformability of (ℳ,ℛ)-systems as a result of environmental alteration. The important concept of strong connectedness is most useful in this direction, and is used to derive a number of results on intertransformability. Some suggestions are made for further studies along these lines.

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Literature

  • Clifford, A. H. and G. B. Preston. 1961.The Algebraic Theory of Semigroups, Vol. I. Mathematical Surveys #7, American Mathematical Society.

  • Ginsburg, S. 1962.An Introduction to Mathematical Machine Theory. Reading: Addison-Wesley Publishing Co., Inc.

    MATH  Google Scholar 

  • Glushkov, V. M. 1961. “The Abstract Theory of Automata.”Russian Mathematical Survey,16, 1–53.

    Article  Google Scholar 

  • Huffman, D. A. 1954. “The Synthesis of Sequential Switching Circuits.”Jour. Franklin Inst.,257, 161–190.

    Article  MATH  MathSciNet  Google Scholar 

  • Moore, E. F. 1956. “Gedanken Experiments on Sequential Machines.”Automata Studies, 129–153, Princeton University Press.

  • Rosen, R. 1958a. “A Relational Theory of Biological Systems.”Bull. Math. Biophysics,20, 245–260.

    Google Scholar 

  • — 1958b. “The Representation of Biological Systems from the Standpoint of the Theory of Categories.”,20, 317–342.

    Google Scholar 

  • — 1959. “A Relational Theory of Biological Systems. II.”,21, 109–128.

    Google Scholar 

  • — 1961. “A Relational Theory of Structural Changes Induced in Biological Systems by Alterations in Environment.”,23, 165–171.

    Google Scholar 

  • — 1962. “A Note on Abstract Relational Biologies.”,24, 31–38.

    MATH  Google Scholar 

  • — 1963a. “On the Reversibility of Environmentally Induced Alterations in Abstract Biological Systems.”,25, 41–50.

    MATH  Google Scholar 

  • — 1963b. “Some Results in Graph Theory and their Application to Abstract Relational Biology.”,25, 231–241.

    MATH  Google Scholar 

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Rosen, R. Abstract biological systems as sequential machines. Bulletin of Mathematical Biophysics 26, 103–111 (1964). https://doi.org/10.1007/BF02476831

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  • DOI: https://doi.org/10.1007/BF02476831

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