Quiescence, Fairness, Testing, and the Notion of Implementation

Two formalisms for concurrency, the Input Output automaton model and the theory of testing, are compared and are shown to have common foundations. The relationship between the fair and quiescent preorders of I O automata is investigated and the two preorders are shown to coincide subject to some restrictions. 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, finitely branching I O automata up to encoding. Conversely, a theory of testing is defined directly on I O automata, and the new reversed must preorder is shown to coincide with the quiescent preorder on strongly convergent, finitely branching I O automata. ] 1997 Academic Press