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Comparing linear and branching time temporal logics

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Temporal Logic in Specification

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 398))

Abstract

An important division of temporal logics is into linear and branching time. Here we propose a general framework for modal and temporal logics and within it offer a formal criterion for distinguishing linear from branching logics. This distinction is based on the CTL* framework. We offer a sound and complete axiomatization of CTL* formulas and we also contrast the general expressiveness of linear and branching time logics.

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References

  1. Abramsky, S. Observation equivalence as a testing equivalence, draft paper, University of London (1985)

    Google Scholar 

  2. Baeten, J., Bergstra, J., Klop, J. ‘Ready trace semantics for concrete process algebra with priority operator', Report CS-R8517. Centrum voor Wiskunde en Informatica (1985).

    Google Scholar 

  3. Brookes, S., Hoare, C. and Roscoe, A. ‘A theory of communicating sequential processes’ JACM pp. 560–591 (1984).

    Google Scholar 

  4. Ben-Ari, M., Manna, Z., and Pnueli, A. ‘The temporal logic of branching time’ in POPI, pp. 164–176 (1981).

    Google Scholar 

  5. Brookes, S., Rounds, W. ‘Behaviour equivalence relations induced by programming logics', LNCS Vol.154 pp.97–108 (1983).

    Google Scholar 

  6. Clarke, E.M., Emerson, E.A. ‘Using branching time temporal logic to synthesize synchronization skeletons’ Science of Computer Programming pp. 241–266 (1982).

    Google Scholar 

  7. DeNicola, R. ‘Testing equivalences and fully abstract models for communicating processes'. University of Edinburgh Ph.D thesis (1985).

    Google Scholar 

  8. De Nicola, R., Hennessy, M. ‘Testing equivalences for processes’ Theoretical Computer Science pp. 83–133 (1984).

    Google Scholar 

  9. Emerson, E.A., Halpern, J., “Sometimes” and ‘not never’ revisited: on branching versus linear time temporal logic. JACM pp. 151–178 (1986)

    Google Scholar 

  10. Emerson, E.A., Lei, C-L., ‘Modalities for model checking: branching time strikes back', In POPL, pp. 84–96 (1985).

    Google Scholar 

  11. Gabbay, D., Pnueli, A., Shelah, A., Stavi, J. ‘The temporal analysis of fairness’ Proc. 7th POPL pp. 163–173 (1980).

    Google Scholar 

  12. Hennessy, M. ‘Axiomatizing finite delay operators' Acta Inform’ pp. 61–88 (1984).

    Google Scholar 

  13. Harel, D., Kozen, D. and Parikh, R. ‘Process logic: expressiveness, decidability, completeness'. J. Comput. System Sci. pp.144–170 (1982).

    Google Scholar 

  14. Hennessy, M., Milner, R. ‘Algebraic laws for nondeterminism and concurrency’ JACM pp. 137–161 (1985).

    Google Scholar 

  15. Hennessy, M., Stirling, C. ‘The power of the future perfect in program logics’ Information and Control pp. 23–52 (1985).

    Google Scholar 

  16. Larsen, K. ‘Proof systems for Hennessy-Milner logic with recursion', draft paper, Aalborg University Centre (1986).

    Google Scholar 

  17. Milner, R. ‘Calculi for synchrony and asynchrony’ Theoretical Computer Science, pp. 267–310 (1983).

    Google Scholar 

  18. Manna Z., and Pnueli, A. ‘How to cook a temporal proof system for your pet language', in POPL pp. 141–154 (1982).

    Google Scholar 

  19. Olderog, E., 'semantics of concurrent processes: the search for structure and abstraction', EATCS Bulletin No.28 pp. 73–97 (1986).

    Google Scholar 

  20. Park, D., ‘Concurrency and automata on infinite sequences’ LNCS Vol.104 (1981).

    Google Scholar 

  21. Phillips, I. ‘Refusal testing’ LNCS Vol. 226 pp.304–313 (1986).

    Google Scholar 

  22. Pnueli, A. ‘Linear and branching structures in the semantics and logics of reactive systems’ LNCS Vol. 194 pp. 14–32 (1985).

    Google Scholar 

  23. Sifakis, J. ‘A unified approach for studying the properties of transition systems'. Theoretical Computer Science pp. 227–258 (1982).

    Google Scholar 

  24. Van Bentham, J. ‘Correspondence theory’ in Vol II of Handbook of Philosophical Logic, ed. Gabbay, D., and Guenthner, F. Reidel, D. pp. 167–247 (1984).

    Google Scholar 

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Authors and Affiliations

  1. Dept. of Computer Science, Edinburgh University, UK

    Colin Stirling

Authors
  1. Colin Stirling
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Editor information

B. Banieqbal H. Barringer A. Pnueli

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© 1989 Springer-Verlag Berlin Heidelberg

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Stirling, C. (1989). Comparing linear and branching time temporal logics. In: Banieqbal, B., Barringer, H., Pnueli, A. (eds) Temporal Logic in Specification. Lecture Notes in Computer Science, vol 398. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51803-7_19

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  • DOI: https://doi.org/10.1007/3-540-51803-7_19

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51803-7

  • Online ISBN: 978-3-540-46811-0

  • eBook Packages: Springer Book Archive

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