When proving the correctness of algorithms in distributed systems, one generally considers safety conditions and liveness conditions. The Input/Output (I/O) automaton model and its timed version have been used successfully, but have focused on safety conditions and on a restricted form of liveness called fairness. In this paper we develop a new I/O automaton model, and a new timed I/O automaton model, that permit the verification of general liveness properties on the basis of existing verification techniques. Our models include a notion of environment-freedom which generalizes the idea of receptiveness of other existing formalisms, and enables the use of compositional verification techniques.

A general automaton model for timing-based systems is presented and is used as the context for developing a variety of simulation proof techniques for such systems. These techniques include (1) refinements, (2) forward and backward simulations, (3) hybrid forward-backward and backward-forward simulations, and (4) history and prophecy relations. Relationships between the different types of simulations, as well as soundness and completeness results, are stated and proved. These results are (with one exception) analogous to the results for untimed systems in Part I of this paper. In fact, many of the results for the timed case are obtained as consequences of the analogous results for the untimed case.