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Realization of Events by Logical Nets

  • Irving M. Copi
  • Calvin C. Elgot
  • Jesse B. Wright

Abstract

In Representation of Events in Nerve Nets and Finite Automata [3], S. C. Kleene obtains a number of interesting results. The most important of these, his analysis and synthesis theorems (theorems 5 and 3), are obscured both by the complexity of his basic concepts and by the nature of the elements used in his nets. In this paper we give a new formulation and new proofs of Kleene’s analysis and synthesis theorems, in which we presuppose no acquaintance with Kleene’s work. We use simpler basic concepts and construct our nets out of more familiar and convenient elements (see section 4). The simplified formulation and proofs should make these important results more widely accessible. Some detailed comments on Kleene’s ideas are made in section 7.

Keywords

Input Sequence Regular Expression Input State Transition Sequence Finite Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    A. W.Burks and H.Wang, The logic of automata, Jour. Assoc. Comp. Mach., Part I: 4 (1957), 193–218MathSciNetGoogle Scholar
  2. [1a]
    A. W.Burks and H.Wang, The logic of automata, Jour. Assoc. Comp. Mach., Part II: 4 (1957), 279–297.MathSciNetGoogle Scholar
  3. [2]
    A. W.Burks and J. B.Wright, Theory of logical nets, Proc. IRE 41 (1953), 1357–1365.CrossRefMathSciNetGoogle Scholar
  4. [3]
    S. C.Kleene, Representation of events in nerve nets and finite automata, Automata Studies, edited by C. E. Shannon and J. McCarthy, Princeton University Press, 1956, pp. 3–41.Google Scholar
  5. [4]
    E. F.Moore, Gedanken-experiments on sequential machines, Automata Studies, edited by C. E. Shannon and J. McCarthy, Princeton University Press, 1956, pp. 129–153.Google Scholar
  6. [5]
    G. H.Mealy, A method for synthesizing sequential circuits, The Bell System Technical Journal, 34 (1955), 1045–1079.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1982

Authors and Affiliations

  • Irving M. Copi
    • 1
  • Calvin C. Elgot
    • 1
  • Jesse B. Wright
    • 1
  1. 1.University of MichiganAnn ArborUSA

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