Quiescence, Fairness, Testing, and the Notion of Implementation (Extended Abstract)

Two diierent formalisms for concurrency are compared and are shown to have common foundations. The Input/Output automaton model and the theory of testing are analyzed in the framework of transition systems. The relationship between the fair and quiescent preorders of I/O automata is investigated and the two preorders are shown to coincide on a large class of automata. I/O automata are encoded into the theory of testing and the reversed must preorder is shown to be equivalent to the quiescent preorder for strongly convergent, nitely branching automata up to encoding. Conversely, a theory of testing is deened directly on I/O automata, and the new reversed must preorder is shown to coincide with the quiescent preorder on strongly convergent, nitely branching automata. Finally, some considerations are given on the issue of divergence, and on other existing theories with an I/O distinction.