On a Certain Generalization of Finite Automata, Which Forms a Hierarchy Analogous to the Grzegorczyk Classification of Primitively Recursive Functions

  • V. A. Kozmidiadi


This paper considers a certain generalization of the notion of a finite automaton. A sequence of expanding classes of n-automata (n = 0, 1, 2, ...) is formed. Each of the classes is formed by closure via a composition in the class of primitive n-automata. Under these conditions a primitive n-automaton operates similarly to a conventional finite automaton: it has an initial state and is stipulated by a certain function of transitions that determine the new state as a function of the previous state and the next input level. However, the states of the automaton are words in the input alphabet; the output word is formed as a sequence of states that are passed through by the automaton due to the action of the input word. The function of transitions for a primitive automaton of the (n + l)-st rank is stipulated by means of an automaton of the n-th rank.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    V. M. Glushkov, “Abstract theory of automata,” Uspekhi Matem. Nauk, Vol. 16, No. 5 (101), pp. 3–62 (1961).MathSciNetGoogle Scholar
  2. 2.
    S. C. Kleeny, Introduction to Mathematics [Russian translation], IL, Moscow (1957).Google Scholar
  3. 3.
    V. A. Kozmidiadi, “On sets which are decidable and enumerable by automata,” Dokl. Akad. Nauk SSSR, 142(5) :1005–1006 (1962).MathSciNetGoogle Scholar
  4. 4.
    V. A. Kozmidiadi, “On sets which are enumerable and decidable by automata,” in: Problems in Logic, Philosophy Institute, Academy of Sciences of the USSR (1963), pp. 102–115.Google Scholar
  5. 5.
    A. A. Markov, Theory of Algorithms, Transactions of the V. A. Steklov Mathematics Institute, Academy of Sciences of the USSR, Vol. 42 (1964).Google Scholar
  6. 6.
    V. A. Trakhtenbrot, Türing Calculations with Logarithmic Delay, Algebra and Logic, 3(4):33–48 (1964).Google Scholar
  7. 7.
    R. Peter, Recursive Functions [Russian translation], IL, Moscow (1954).Google Scholar
  8. 8.
    V. S. Chernyavskii, On a Certain Class of Normal Markov Algorithms, in: Logic Investigations, Philosophy Institute, Academy of Sciences of the USSR (1959), pp. 263–299.Google Scholar
  9. 9.
    A. Grzegorczyk, “Some classes of recursive functions,” Rozprawy Matematyczne (Warsaw), Vol. 4 (1953).MATHGoogle Scholar

Copyright information

© Consultants Bureau, New York 1973

Authors and Affiliations

  • V. A. Kozmidiadi
    • 1
  1. 1.MoscowRussia

Personalised recommendations