The decomposition of the regular asynchronous systems as parallel connection of regular asynchronous systems

The asynchronous systems are the non-deterministic models of the asynchronous circuits from the digital electrical engineering, where non-determinism is a consequence of the fact that modelling is made in the presence of unknown and variable parameters. Such a system is a multi-valued function f that assigns to an (admissible) input u : R! f0; 1gm a set f(u) of (possible) states x : R! f0; 1gn: When this assignment is de…ned by making use of a so-called generator function : f0; 1gn f0; 1gm ! f0; 1gn; then the asynchronous system f is called regular. The generator function acts in this asynchronous framework similarly with the next state function from a synchronous framework. The parallel connection of the asynchronous systems f 0 and f 00 is the asynchronous system (f 0jjf 00)(u) = f 0(u) f 00(u): The purpose of the paper is to give the circumstances under which a regular asynchronous system f may be written as a parallel connection of regular asynchronous systems.