A Study of Feedback and Errors in Sequential Machines

The object of this paper is to study feedback in sequential machines, to classify (according to their seriousness) and analyze errors which arise in the state transitions of machines, and to establish some relations between feedback and errors. It is shown that the previously developed algebraic methods1,2 supply the necessary tools and a rigorous basis for this theory, and relate these new results to previously obtained results about the structure of sequential machines. For example, this work yields the necessary methods to detect the existence of a decomposition of machines into component machines so that the most ``serious´´ errors of the computation can occur only in an isolated component machine. This leads to the possibility of imposing selectively different reliability conditions on the component machines to achieve high over-all reliability of the realizations.