Asynchronous composition and required security conditions

We propose a general model of representation of systems which takes into account asynchronous systems. We show that, as non deducibility on strategies, the causality property is also a hook-up property and we generalize this result to the case of asynchronous machines. The two basic operations we use to represent hook-up-direct product and feedback-are generalizations of the classic operations already defined in case of synchronous systems. Our direct product operation allows us to combine two systems having different clocks and our feedback operation can be used to analyze the security of systems where inputs might be blocked.<>