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Theory of Algorithms and Discrete Processors

Chapter

Abstract

It is usual today to define cybernetics as the science of the general laws of information processing in complex systems.

Keywords

Output Function Turing Machine Terminal State Finite Automaton Transition Graph 
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.
    Ya. M. Barzdin’, Universal Pulsing Elements, Dokl. Akad. Nauk SSSR 157 (2), 291–294 (1964)Google Scholar
  2. 2.
    Ya. M. Barzdin’, Universality Problem in the Theory of Growing Automata, Dokl. Akad. Nauk SSSR 157 (3), 542–544 (1964)Google Scholar
  3. 3.
    V. G. Bodnarchuk, Metric Space of Events, I, Zh. Kibemetika, No. 1 (1965)Google Scholar
  4. 4.
    V. G. Bodnarchuk, Metric Space of Events, II, Zh. Kibemetika, No. 4 (1965)Google Scholar
  5. 5.
    N. I. Glebov, Synthesis of Operators, in “Problems of Cybernetics,” Vol. 8, pp. 191–200 (in Russian) (1962)Google Scholar
  6. 6.
    N. I. Glebov, Algebraic Equivalence of Subsets of Categories, in “Problems of Cybernetics,” Vol. 8, pp. 201–209 (in Russian) (1962)Google Scholar
  7. 7.
    V. M. Glushkov, Automata Theory and Questions in Designing Digital Machine Structures, Zh. Kibernetika, No. 1 (1965)Google Scholar
  8. 8.
    V. M. Glushkov, Automata Theory and Formal Transformations of Microprograms, Zh. Kibernetika, No. 5 (1965)Google Scholar
  9. 9.
    V. M. Glushkov, Minimization of Microprograms and Schemes of Algorithms, Zh. Kibernetika, No. 5 (1966)Google Scholar
  10. 10.
    V. M. Glushkov, Defining Relationships in Two-Adder Operational Devices, Zh. Kibernetika, No. 1 (1968)Google Scholar
  11. 11.
    V. M. Glushkov, “Mathematics and Cybernetics” (in Russian), in “Nauchnye Misl.” APN (1968)Google Scholar
  12. 12.
    V. M. Glushkov, Abstract Theory of Automata, Usp. Matem. Nauk 16 (5), 3–62 (1961)Google Scholar
  13. 13.
    V. K. Detlovs, Equivalence of Normal Algorithms and Recursive Functions, Tr. V. A. Steklov Mathematical Institute 2, 5–142 (1958)Google Scholar
  14. 14.
    A. P. Ershov, Operator Algorithms, I, in “Problems of Cybernetics,” Vol. 3, pp. 5–48 (in Russian) (1960)Google Scholar
  15. 15.
    A. P. Ershov, Operator Algorithms, II, in “Problems of Cybernetics,” Vol. 8, pp. 211–233 (in Russian) (1962)Google Scholar
  16. 16.
    I. D. Zaslavskii, Graph Schemes with Memory, Tr. V. A. Steklov Mathematical Institute 22, 99–192 (1964)Google Scholar
  17. 17.
    L. A. Kaluzhnin, Algorithmization of Mathematical Problems, in “Problems of Cybernetics,” Vol. 2, pp. 51–67 (in Russian) (1959)Google Scholar
  18. 18.
    A. N. Kolmogorov and V. A. Uspenskii, On the Definition of Algorithm, Usp. Matem. Nauk 13 (4), 3–28 (1958)Google Scholar
  19. 19.
    A. N. Kolmogorov, Three Approaches to Defining the Concept of “quantity of information,” Problemy Peredachi Informatsii 1, 3–11 (1965)Google Scholar
  20. 20.
    V. S. Korolyuk, The Concept of an Address Algorithm, in “Problems of Cybernetics,” Vol. 4, pp. 95–110 (in Russian) (1960)Google Scholar
  21. 21.
    A. A. Letichevskii, Equivalence of Automata with Terminal States, I, Zh. Kibernetika, No. 4 (1966)Google Scholar
  22. 22.
    A. A. Letichevskii, Equivalence of Automata with Terminal States, II, Zh. Kibernetika, No. 1 (1967)Google Scholar
  23. 23.
    A. A. Lyapunov, Logical Schemes of Programs, in “Problems of Cybernetics,” Vol. 1, pp. 46–74 (in Russian) (1958)Google Scholar
  24. 24.
    A. A. Lyapunov, The Algebraic Treatment of Programming, in “Problems of Cybernetics,” Vol. 8, pp. 235–241 (in Russian) (1962)Google Scholar
  25. 25.
    A. A. Markov, “Theory of Algorithms.,” Published as Trudy V. A. Steklov Mathematical Institute 12 (1954)Google Scholar
  26. 26.
    V. A. Nepomnyashchii, Certain Automata Capable of Computing Bases for Recursively Enumerable Sets, Algebra i Logika 5 (5), 69–83 (1966)Google Scholar
  27. 27.
    R. I. Podlovchenko, System of Programming Concepts, Dokl. Akad. Nauk SSSR 132 (6), 1287–1290 (1960)Google Scholar
  28. 28.
    R. I. Podlovchenko, Transformations of Programming Schemes and their Application to Programming, in “Problems of Cybernetics,” Vol. 7, pp. 161–188 (in Russian) (1962)Google Scholar
  29. 29.
    R. N. Tonoyan, Logical Schemes of Algorithms and their Equivalent Transformations, in “Problems of Cybernetics,” Vol. 14, pp. 161–188 (in Russian) (1965)Google Scholar
  30. 30.
    B. A. Trakhtenbrot, “Complexity of Algorithms and Computations,” Novosibirsk (1967)Google Scholar
  31. 31.
    R. V. Freivald, The Order of Growth of Exact Temporal Signalling for Turing Computations, Algebra i Logika, Seminar 5, 85–93 (1966)Google Scholar
  32. 32.
    L. A. Sholomov, Complexity Criteria for Boolean Functions, in “Problems of Cybernetics,” Vol. 17, pp. 91–127 (in Russian) (1966)Google Scholar
  33. 33.
    Yu. I. Yanov, Logical Schemes of Algorithms, in “Problems of Cybernetics,” Vol. 1, pp. 75–127 (in Russian) (1958)Google Scholar
  34. 34.
    H. Thiele, “Epistemological Investigations in Algorithmic Languages,” I (in German), Berlin (1966)Google Scholar
  35. 35.
    J. W. Backus, F. L. Bauer, J. Green, C. Katz, J. McCarthy, P. Naur (ed.), A. J. Perlis, H. Rutishauser, K. Samuelson, B. Vauquois, G. H. Wagstein, A. van Wijngaarden, and M. Woodger, Report on the Algorithmic Language algol 60, Numerische Math. 2 (2), 106–139 (1960)Google Scholar
  36. 36.
    M. Blum, A Machine-Independent Theory of the Complexity of Recursive Functions, J. Assoc. Comp. Mach. 14, 322–337 (1967)CrossRefGoogle Scholar
  37. 37.
    A. W. Burks, Computation, Behavior, and Structure in Fixed and Growing Automata, University of Michigan Technical Report under O.N.R. Contract 1224 (21) (1959)Google Scholar
  38. 38.
    F. B. Cannonito, Hierarchies of Computable Groups and the Word Problem, J. Symbolic Logic 31 (3), 376–392 (1966)CrossRefGoogle Scholar
  39. 39.
    A. Church, An Unsolvable Problem of Elementary Number Theory, Amer. J. Math. 58, 345–363 (1936)CrossRefGoogle Scholar
  40. 40.
    M. Davis, “Computability and Unsolvability,” McGraw-Hill Book Co., New York (1958)Google Scholar
  41. 41.
    K. Gödel, Formally Undecidable Theorems of the “Principia Mathematica” and Applied Systems, I, Monatshefte Math. u. Physik 38, 173–198 (1931)CrossRefGoogle Scholar
  42. 42.
    J. Hartmanis and R. E. Stearns, On the Computational Complexity of Algorithms, Trans. Amer. Math. Soc. 117, 285–306 (1965)CrossRefGoogle Scholar
  43. 43.
    F. C. Hennie, One-Tape Off-Line Turing Machine Computations, Information Control 8 (6), 553–578 (1965)CrossRefGoogle Scholar
  44. 44.
    F. C. Hennie, “Iterative Arrays of Logical Circuits,” MIT Press, Cambridge, Mass. and John Wiley and Sons, New York (1961)Google Scholar
  45. 45.
    F. C. Hennie and R. E. Stearns, Two-Tape Simulation of Multitape Turing Machines, J. Assoc. Comp. Mach. 13, 533–546 (1966)CrossRefGoogle Scholar
  46. 46.
    J. H. Holland, Iterative Circuit Computers, in “Proceedings of the 1960 Joint Computer Conference.”Google Scholar
  47. 47.
    S. C. Kleene, On Notation for Ordinal Numbers, J. Symbolic Logic 3, 150–155 (1938)CrossRefGoogle Scholar
  48. 48.
    S. C. Kleene, “Introduction to Metamathematics,” D. Van Nostrand Co., Princeton, N. J. (1952)Google Scholar
  49. 49.
    S. C. Kleene, λ-Definability and Recursiveness, Duke Math. J. 2, 340–353 (1936)CrossRefGoogle Scholar
  50. 50.
    J. McCarthy, Towards a Mathematical Science of Computation, in “Proceedings of the IFIP Congress” (1962)Google Scholar
  51. 51.
    E. F. Moore, Machine Models of Self-Reproduction, in “Proceedings of the October Meeting of the American Math. Soc, Cambridge, Mass.,” pp. 560–562 (1959)Google Scholar
  52. 52.
    E. L. Post, Finite Combinatory Processes-Formulation I, J. Symbolic Logic 1, 103–105 (1936)CrossRefGoogle Scholar
  53. 53.
    A. M. Turing, “On Computable Numbers with an Application to the Entscheidungs-problem,” Proc. London Math. Soc, Series 2, 42, 230–265 (1936-7)CrossRefGoogle Scholar
  54. 54.
    A. M. Turing, A Correction, Proc. London Math. Soc, series 2, 43, 544–546 (1937)CrossRefGoogle Scholar
  55. 55.
    A. M. Turing, Computability and λ-Definability, J. Symbolic Logic 2, 153–163 (1937)CrossRefGoogle Scholar
  56. 56.
    J. D. Rutledge, On Janov’s Program Schemata, J. Assoc Comp. Mach. 11 (1) (1964)Google Scholar

Copyright information

© Plenum Press 1969

Authors and Affiliations

  1. 1.Institute of CyberneticsThe Ukrainian Academy of SciencesKievUkrainian SSR

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