Finite Automata with Multiset Memory: A New Characterization of Chomsky Hierarchy

Abstract

This paper concerns new characterizations of language classes in the Chomsky hierarchy in terms of a new type of computing device called FAMM (Finite Automaton with Multiset Memory) in which a multiset of symbol objects is available for the storage of working space. Unlike the stack or the tape for a storage, the multiset might seem to be less powerful in computing task, due to the lack of positional (structural) information of stored data. We introduce the class of FAMMs of degree d (for non-negative integer d) in general form, and investigate the computing powers of some subclasses of those FAMMs. We show that the classes of languages accepted by FAMMs of degree 0, by FAMMs of degree 1, by exponentially-bounded FAMMs of degree 2, and by FAMMs of degree 2 are exactly the four classes of languages REG, CF, CS and RE in the Chomsky hierarchy, respectively. Thus, this unified view from multiset-based computing provides new insight into the computational aspects of the Chomsky hierarchy.

Theory of reaction automata: a survey

“…For the purpose to explore the computational capability of the multiset storage working under the finite-state controller, a new type of finite automata with multiset memory (named FAMMs) were introduced in [55].…”

“…Specifically, the following has been established in [55]: The classes of languages accepted by FAMMs of degree 0, by FAMMs of degree 1, by exponentially-bounded FAMMs of degree 2, and by FAMMs of degree 2 are exactly the four classes of languages REG, CF, CS and RE in the Chomsky hierarchy, respectively.…”

“…This survey is largely based on the achievements of research on RAs in the source references [51][52][53][54][55][56][58][59][60], and primarily discusses the computational capabilities of RAs in two application manners: the maximally parallel manner (first employed in [52,53]) and the sequential manner (mainly considered in [51,56]). Note that application manners are referred to as "evolution modes" or "update modes" in some literature.…”