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.
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