A structural property of regular frequency computations

Abstract

AbstractThe notion of an (m,n)-computation was already introduced in 1960 by Rose and further investigated by Trakhtenbrot in 1963. It has been extended to finite automata by Kinber in 1976 and he has shown an analogue of Trakhtenbrot's result: The class of languages (m,n)-recognizable by deterministic finite automata is equal to the class of regular languages if and only if 2m>n. Furthermore, for a unary alphabet, the class of (m,n)-recognizable languages coincides with the class of regular languages for all m and n. In this paper, we will present the first structural property of (m,n)-recognizable languages which is valid for all 1⩽m⩽n and for all alphabets. Kinber's result for unary alphabets becomes a corollary. This property is also used to show that certain non-unary languages are not (m,n)-regular and that the class of all (m,n)-recognizable languages is not closed under the reversal operation. However, this class forms a Boolean algebra