On n-type finite state acceptors

Abstract

Certain properties of three variants of the multi-tape automata of Rabin and Scott are proved. Closure properties of the defined sets of n-tuples are found, and the nature of projections of the defined sets of n-tuples on one coordinate is studied. Some necessary conditions for acceptance are derived, and a characterization of the sets of n-tuples defined by non-deterministic n-tape automata is found. The results in the paper generalize and supplement the results of Rabin and Scott.