Temporal verification of simulation and refinement

Yonit Kesten, Zohar Manna, Amir Pnueli

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

41 Scopus citations

Abstract

The paper presents temporal logic methods for proving simulation and refinement relations between programs. After introducing the notions of fai~ 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 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 TLt~. 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 TLI%. 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.

Original languageEnglish
Title of host publicationA Decade of Concurrency
Subtitle of host publicationReflections and Perspectives - REX School/Symposium, Proceedings
EditorsJ.W. de Bakker, W.-P. de Roever, G. Rozenberg
PublisherSpringer Verlag
Pages273-346
Number of pages74
ISBN (Print)9783540580430
DOIs
StatePublished - 1 Jan 1994
Externally publishedYes
Event7th REX School/Symposium on Decade of Concurrency, 1993 - Noordwijkerhout, Netherlands
Duration: 1 Jun 19934 Jun 1993

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume803 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference7th REX School/Symposium on Decade of Concurrency, 1993
Country/TerritoryNetherlands
CityNoordwijkerhout
Period1/06/934/06/93

Keywords

  • Invariance
  • Reactivity
  • Refinement
  • Response
  • Simulation
  • Stuttering
  • Temporal logic
  • Verification of properties

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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