Skip to main content
Springer Nature Link
Log in

How linear can branching-time be?

  • Conference paper
  • First Online:
Temporal Logic (ICTL 1994)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 827))

Included in the following conference series:

Abstract

We suggest a new characterization that draws finer lines between branching-time and linear-time formulas of the logic CTL*. We define three types of linearity, strong linearity, sub-linearity and equi-linearity, each of which contains all LTL formulas. We prove that these notions are distinct. Moreover, strong linearity implies sub-linearity which implies equi-linearity. We investigate these notions over Kripke structures with and without fairness and show that they do not coincide. We give a syntactic characterization for linear ∀CTL* formulas. Finally, we discuss the practical implication of the new characterization.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. C. Browne, E. M. Clarke, and O. Grumberg. Characterizing finite Kripke structures in propositional temporal logic. Theoretical Computer Science, 59(1–2), July 1988.

    Google Scholar 

  2. E. M. Clarke and I. A. Draghicescu. Expressibility results for linear time and branching time logics. In Linear Time, Branching Time, and Partial Order in Logics and Models for Concurrency, volume 354, pages 428–437. Springer-Verlag: Lecture Notes in Computer Science, 1988.

    Google Scholar 

  3. E. M. Clarke and E. A. Emerson. Synthesis of synchronization skeletons for branching time temporal logic. In Logic of Programs: Workshop, Yorktown Heights, NY, May 1981, volume 131 of Lecture Notes in Computer Science. Springer-Verlag, 1981.

    Google Scholar 

  4. E. M. Clarke, E. A. Emerson, and A. P. Sistla. Automatic verification of finitestate concurrent systems using temporal logic specifications. In Proceedings of the Tenth Annual A CM Symposium on Principles of Programming Languages, January 1983.

    Google Scholar 

  5. E. M. Clarke, O. Grumberg, and D. E. Long. Model checking and abstraction. In Proceedings of the Nineteenth Annual ACM Symposium on Principles of Programming Languages, January 1992.

    Google Scholar 

  6. D. Dams, O. Grumberg, and R. Gerth. Generation of reduced models for checking fragments of CTL. In C. Courcoubetis, editor, Proceedings of the Fifth Workshop on Computer-Aided Verification, volume 697 of Lecture Notes in Computer Science. Springer-Verlag, July 1993.

    Google Scholar 

  7. E. A. Emerson and J. Y. Halpern. “Sometimes” and “Not Never” revisited: On branching time versus linear time. Journal of the ACM, 33:151–178, 1986.

    Article  Google Scholar 

  8. E. A. Emerson and C.-L. Lei. Modalities for model checking: Branching time strikes back. In POPL85 [17].

    Google Scholar 

  9. O. Grumberg and D. E. Long. Model checking and modular verification. To appear in ACM Transactions on Programming Languages and Systems.

    Google Scholar 

  10. Z. Har'El and R. P. Kurshan. The COSPAN user's guide. Technical Report 11211-871009-21TM, AT & T Bell Laboratories, 1987.

    Google Scholar 

  11. Z. Har'El and R. P. Kurshan. Software for analytical development of communications protocols. AT & T Technical Journal, 69(1):45–59, Jan.–Feb. 1990.

    Google Scholar 

  12. R. P. Kurshan. Analysis of discrete event coordination. In J. W. de Bakker, W.-P. de Roever, and G. Rozenberg, editors, Proceedings of the REX Workshop on Stepwise Refinement of Distributed Systems, Models, Formalisms, Correctness, volume 430 of Lecture Notes in Computer Science. Springer-Verlag, May 1989.

    Google Scholar 

  13. O. Lichtenstein and A. Pnueli. Checking that finite state concurrent programs satisfy their linear specification. In POPL85 [17].

    Google Scholar 

  14. R. Milner. An algebraic definition of simulation between programs. In Proceedings of the Second International Joint Conference on Artificial Intelligence, September 1971.

    Google Scholar 

  15. R. Milner. A Calculus of Communicating Systems, volume 92 of Lecture Notes in Computer Science. Springer-Verlag, 1980.

    Google Scholar 

  16. A. Pnueli. A temporal logic of concurrent programs. Theoretical Computer Science, 13:45–60, 1981.

    Article  Google Scholar 

  17. Proceedings of the Twelfth Annual ACM Symposium on Principles of Programming Languages, January 1985.

    Google Scholar 

  18. J.P. Quielle and J. Sifakis. Specification and verification of concurrent systems in CESAR. In Proceedings of the Fifth International Symposium in Programming, 1981.

    Google Scholar 

  19. G. Shurek and O. Grumberg. The modular framework of computer-aided verification: Motivation, solutions and evaluation criteria. In R. P. Kurshan and E. M. Clarke, editors, Proceedings of the 1990 Workshop on Computer-Aided Verification, June 1990.

    Google Scholar 

  20. M. Y. Vardi and P. Wolper. An automata-theoretic approach to automatic program verification. In Proceedings of the First Annual Symposium on Logic in Computer Science. IEEE Computer Society Press, June 1986.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, The Technion, 32000, Haifa, Israel

    Orna Grumberg

  2. AT & T Bell Laboratories, 07974, Murray Hill, NJ, USA

    Robert P. Kurshan

Authors
  1. Orna Grumberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Robert P. Kurshan
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Dov M. Gabbay Hans Jürgen Ohlbach

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Grumberg, O., Kurshan, R.P. (1994). How linear can branching-time be?. In: Gabbay, D.M., Ohlbach, H.J. (eds) Temporal Logic. ICTL 1994. Lecture Notes in Computer Science, vol 827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013988

Download citation

  • DOI: https://doi.org/10.1007/BFb0013988

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58241-0

  • Online ISBN: 978-3-540-48585-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics