Abstract
The paper presents temporal logic methods for proving simulation and refinement relations between programs. After introducing the notions of fair transition systems and the specification language of temporal logic, we present proof rules for verifying properties of programs. We then define the relations of simulation and refinement between programs and relate them to inclusion relations between computations and observations of the compared systems.
We then show that these semantic definitions can be formalized in temporal logic by the use of the temporal and observational semantics formulas. This representation expresses simulation and refinement 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, 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 sarnpling 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 refinement, and illustrate its use to prove refinement of two programs that cannot be done within the regular temporal logic framework.
This research was supported in part by the National Science Foundation under grant CCR-92-23226, by the Defense Advanced Research Projects Agency under contract NAG2-703, by the United States Air Force Office of Scientific Research under contract F49620-93-1-0139, by the European Community ESPRIT Basic Research Action Project 6021 (REACT), and by the France-Israel project for cooperation in Computer Science.
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Kesten, Y., Manna, Z., Pnueli, A. (1994). Temporal verification of simulation and refinement. In: de Bakker, J.W., de Roever, W.P., Rozenberg, G. (eds) A Decade of Concurrency Reflections and Perspectives. REX 1993. Lecture Notes in Computer Science, vol 803. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58043-3_22
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DOI: https://doi.org/10.1007/3-540-58043-3_22
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