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 : R → {0, 1}m a set f(u) of possible states x ∈ f(u), x : R → {0, 1}n. A special case of asynchronous system consists in the existence of a Boolean function Υ : {0, 1}n × {0, 1}m → {0, 1}n such that ∀u, ∀x ∈ f(u), a certain equation involving Υ is fulfilled. Then Υ is called the generator function of f (Moisil used the terminology of network function) and we say that f is generated by Υ. 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].