Temporal Veriication of Simulation and Reenement ?

The paper presents temporal logic methods for proving simulation and reenement relations between programs. After introducing the notions of fair transition systems and the speciication language of temporal logic, we present proof rules for verifying properties of programs. We then deene the relations of simulation and reenement between programs and relate them to inclusion relations between computations and observations of the compared systems. We then show that these semantic deenitions can be formalized in temporal logic by the use of the temporal and observational semantics formulas. This representation expresses simulation and reenement as implications between a pair of such formulas. We provide proof rules, based on the rules for verifying program properties. The proof rules are illustrated on several simple examples. Towards the end of the rst part, we recognize the usefulness of having a stuttering-robust version of temporal logic. The second part of the paper presents a proposed temporal logic, called TLR, which is insensitive to stuttering. This logic is interpreted over sequences of sampling points, alternating between persistent and transient sample points. This logic possesses an idempotent next-time operator, which gives some insight into its stuttering robustness. We present a decision procedure and a complete axiomatic system for the propositional version of TLR. It is shown that, if all system variables are taken to be left-continuous, then most of the rules of regular temporal logic are still sound for TLR. Finally, we present a stronger proof rule for reenement, and illustrate its use to prove reenement of two programs that cannot be done within the regular temporal logic framework.