Some properties of the regular asynchronous systems

The asynchronous systems are the models of the asynchronous circuits from the digital electrical engineering. An asynchronous system f is a multi-valued function that assigns to each admissible input u a set f(u) of possible states x in f(u). A special case of asynchronous system consists in the existence of a Boolean function \Upsilon such that for any u and any x in f(u), a certain equation involving \Upsilon is fulfilled. Then \Upsilon is called the generator function of f (Moisil used the terminology of network function) and we say that f is generated by \Upsilon. The systems that have a generator function are called regular. Our purpose is to continue the study of the generation of the asynchronous systems that was started in [2], [3].