Some Properties of the Regular Asynchronous Systems

Abstract: 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]