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Automata Theory as an Abstract Boundary Condition for the Study of Information Processing in the Nervous System

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Abstract

This conference convenes 25 years after Warren McCulloch and Walter Pitts (1943) initiated the automaton-theoretic approach to information processing in the nervous system with their paper “A Logical Calculus of the Ideas Immanent in Nervous Activity,” and a few weeks before Warren McCulloch celebrates his 70th birthday. I should thus like to dedicate this paper to Warren McCulloch, in honor of his continuing stimulation to many who would understand “What’s in the Brain that Ink may Character?” [McCulloch, 1965].

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References

  • Arbib, M. A. (1964). Brains, machines and mathematics. New York: McGraw-Hill.

    Google Scholar 

  • Arbib, M. A. (ed.) (1968). Algebraic theory of machines, languages and semigroups. New York: Academic Press.

    Google Scholar 

  • Arbib, M. A. (1969). Theories of abstract automata. Englewood Cliffs: Prentice-Hall.

    Google Scholar 

  • Arbib, M. A. (in press a). Memory limitations of stimulus-response models. Psych. Rev.

    Google Scholar 

  • Arbib, M. A. (in press). The metaphorical brain. Englewood Cliffs: Prentice-Hall.

    Google Scholar 

  • Arbib, M. A. and Zeiger, H. P. (1969). On the relevance of abstract algebra to control theory. Automatica.

    Google Scholar 

  • Barzdin, Y. M. (1965). Complexity of recognition of symmetry in Turing machines. Problemy Kibernetiki, 15.

    Google Scholar 

  • Davis, M., (ed.) (1965). The undecidable. Hewlett: Raven Press.

    Google Scholar 

  • Gödel, K. (1931). Über formal unentscheidbare Sätze der Principia Mathe-matica und verwandter Systeme I. Monatshefte fur Mathematik und Physik, 38: 173–198.

    Article  Google Scholar 

  • Gödel, K. (1936). Über die Länge der Beweise. Ergeb. eines math. Kolloquiums, 7: 23–24.

    Google Scholar 

  • Hartmanis, J. and Stearns, R. E. (1966). Algebraic theory of sequential machines. Englewood Cliffs: Prentice-Hall.

    Google Scholar 

  • Hubel, D. H. and Wiesel, T. N. (1962). Receptive fields, binocular interaction, and functional architecture in the cat’s visual cortex. J. Physiol., 160: 106–154.

    PubMed  CAS  Google Scholar 

  • Lettvin, J., Maturana, H., McCulloch, W. S. and Pitts, W. (1959). What the frog’s eye tells the frog’s brain. Proc. IRE, 47: 1940–1951.

    Article  Google Scholar 

  • McCulloch, W. S. (1965). What’s in the brain that ink may character? In W. S. McCulloch, Embodiments of mind. Cambridge: MIT Press.

    Google Scholar 

  • McCulloch, W. S. and Pitts, W. (1943). A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biophys., 5: 115–133.

    Article  Google Scholar 

  • Miller, G. A., Galanter, E. and Pribram, K. H. (1960). Plans and the structure of behavior. New York: Holt, Rinehart and Winston, Inc.

    Book  Google Scholar 

  • Minsky, M. L. (1961). Steps toward artificial intelligence. Proc. IRE, 49 (1): 8–30.

    Article  Google Scholar 

  • Minsky, M. L. (1967). Computation: finite and infinite machines. Englewood Cliffs: Prentice-Hall.

    Google Scholar 

  • Minsky, M. L. and Papert, S. (1967). Linearly unrecognizable patterns, in Mathematical aspects of computer science, Vol. XIX of Proceedings of Symposia in Applied Mathematics. Providence: Amer. Math. Soc. 176–217.

    Google Scholar 

  • Moore, E. F. (1956). Gedanken-experiments on sequential machines. In C. E. Shannon and J. McCarthy, (eds.), Automata studies. Princeton: Princeton University Press. 129–153.

    Google Scholar 

  • Post, E. L. (1936). Finite combinatory processes—formulation I. J. Symbolic Logic, 1: 103–105.

    Article  Google Scholar 

  • Ritchie, R. W. (1963). Classes of predictably computable functions. Trans. Am. Math. Soc., 106: 139–173.

    Article  Google Scholar 

  • Shannon, C. E. and McCarthy, J., eds. (1956). Automata studies. Princeton: Princeton University Press.

    Google Scholar 

  • Spira, P. M. (1968). On the computational complexity of finite functions. Unpublished Ph.D. Thesis, Dept. of Electrical Engineering, Stanford University.

    Google Scholar 

  • Spira, P. M. and Arbib, M. A. (1967). Computation times for finite groups, semigroups and automata. Proc. IEEE 8th Ann. Symp. Switching and Automata Theory, 291–295.

    Google Scholar 

  • Suppes, P. (1968). Stimulus-response theory of finite automata. Technical Report No. 133, Psychology Series, Institute for Math. Studies in the Social Sciences, Stanford University.

    Google Scholar 

  • Turing, A. M. (1936). On computable numbers with an application to the Entscheidungs-problem. Proc. London Math. Soc., Ser. 2–42: 230–265; with a correction, Ibid., 43 (1936–7): 544–546.

    Google Scholar 

  • Wang, H. (1957). A variant to Turing’s theory of computing machines. J. Assoc. Comp. Math., 4: 63–92.

    Article  Google Scholar 

  • Winograd, S. (1967). On the time required to perform multiplication. J. ACM, 14: 793–802.

    Article  Google Scholar 

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Arbib, M.A. (1969). Automata Theory as an Abstract Boundary Condition for the Study of Information Processing in the Nervous System. In: Leibovic, K.N. (eds) Information Processing in The Nervous System. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-25549-0_1

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  • DOI: https://doi.org/10.1007/978-3-662-25549-0_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-23480-8

  • Online ISBN: 978-3-662-25549-0

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