On a Certain Generalization of Finite Automata, Which Forms a Hierarchy Analogous to the Grzegorczyk Classification of Primitively Recursive Functions
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.
- 1.V. M. Glushkov, “Abstract theory of automata,” Uspekhi Matem. Nauk, Vol. 16, No. 5 (101), pp. 3–62 (1961).Google Scholar
- 2.S. C. Kleeny, Introduction to Mathematics [Russian translation], IL, Moscow (1957).Google Scholar
- 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.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
- 7.R. Peter, Recursive Functions [Russian translation], IL, Moscow (1954).Google Scholar
- 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.A. Grzegorczyk, “Some classes of recursive functions,” Rozprawy Matematyczne (Warsaw), Vol. 4 (1953).Google Scholar