Skip to main content

The Stuttering Principle Revisited: On the Expressiveness of Nested X and ⋃ Operators in the Logic LTL

  • Conference paper
  • First Online:
Computer Science Logic (CSL 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2471))

Included in the following conference series:

  • 599 Accesses

  • 5 Citations

Abstract

It is known that LTL formulae without the ‘next’ operator are invariant under the so-called stutter-equivalence of words. In this paper we extend this principle to general LTL formulae with given nesting depths of the ‘next’ and ‘until’ operators. This allows us to prove the semantical strictness of three natural hierarchies of LTL formulae, which are parametrized either by the nesting depth of just one of the two operators, or by both of them. As another interesting corollary we obtain an alternative characterization of LTL languages, which are exactly the regular languages closed under the generalized form of stutter equivalence. We also indicate how to tackle the state-space explosion problem with the help of presented results

Supported by the Grant Agency of Czech Republic, grant No. 201/00/1023.

Supported by the Grant Agency of Czech Republic, grant No. 201/00/0400, and by a grant FRVŠ No. 601/2002.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. E.M. Clark, O. Grumberg, and D.A. Peled. Model Checking. The MIT Press, 1999.

    Google Scholar 

  2. K. Etessami and T. Wilke. An until hierarchy and other applications of an Ehrenfeucht-FraΫissé game for temporal logic. Information and Computation, 160:88–108, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  3. H. Kamp. Tense Logic and the Theory of Linear Order. PhD thesis, UCLA, 1968.

    Google Scholar 

  4. L. Lamport. What good is temporal logic? In Proceedings of IFIP Congress on Information Processing, pages 657–667, 1983.

    Google Scholar 

  5. R. McNaughton and S. Papert. Counter-Free Automata. The MIT Press, 1971.

    Google Scholar 

  6. A. Pnueli. The temporal logic of programs. In Proceedings of 18th Annual Symposium on Foundations of Computer Science, pages 46–57. IEEE Computer Society Press, 1977.

    Google Scholar 

  7. W. Thomas. Automata on infinite objects. Handbook of Theoretical Computer Science, B:135–192, 1991.

    Google Scholar 

  8. T. Wilke. Classifying discrete temporal properties. In Proceedings of STACS’99, volume 1563 of LNCS, pages 32–46. Springer, 1999.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kucera, A., Strejček, J. (2002). The Stuttering Principle Revisited: On the Expressiveness of Nested X and ⋃ Operators in the Logic LTL. In: Bradfield, J. (eds) Computer Science Logic. CSL 2002. Lecture Notes in Computer Science, vol 2471. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45793-3_19

Download citation

  • DOI: https://doi.org/10.1007/3-540-45793-3_19

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44240-0

  • Online ISBN: 978-3-540-45793-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics