Systems of Asynchronously Operating Modules

This note considers the operation of systems composed of interconnected asynchronously operating modules and shows that some such systems may enter "blocking conditions" in which no module can change state. The model considered applies specifically to asynchronous systems in which each module is controlled only by its neighbors, but may also be relevant to other systems such as parallel computational schemes. We also demonstrate a procedure that may speed up computation and we show that the function computed by a given network may depend upon the initial state.