Multiset Processing by Means of Systems of Finite State Transducers

We introduce a computing mechanism of a biochemical inspiration (similar to a P system from the area of Computing with Membranes) which consists of a multiset of symbol-objects and a set of finite state transducers. The transducers process symbols in the current multiset in the usual manner. A computation starts in an initial configuration and ends in a halting configuration. The power of these mechanisms is investigated, as well as the closure properties of the obtained family. The main results say that (1) systems with two components and an unbounded number of states in each component generate all gsm images of all permutation closures of recursively enumerable languages, while (2) systems with two states in each component but an unbounded number of components can generate the permutation closures of all recursively enumerable languages, and (3) the obtained family is a full AFL. Result (2) is related to a possible (speculative) implementation of our systems in biochemical media.