Forward and Backward Simulations Part I: Untimed Systems

A uni ed, comprehensive presentation of simulation techniques for veri cation of concurrent systems is given, in terms of a simple untimed automaton model. In particular, (1) re nements, (2) forward and backward simulations, (3) hybrid forward-backward and backward-forward simulations, and (4) history and prophecy relations are de ned. History and prophecy relations are abstract versions of the history and prophecy variables of Abadi and Lamport, as well as the auxiliary variables of Owicki and Gries. Relationships between the di erent types of simulations, as well as soundness and completeness results, are stated and proved. Finally, it is shown how invariants can be incorporated into all the simulations. The development for untimed automata is designed to support a similar development for timed automata. In Part II of this paper, it is shown how the results of this paper can be carried over to the setting of timed automata. 1991 Mathematics Subject Classi cation: 68Q60, 68Q68. 1991 CR Categories: F.1.1, F.3.1.