Skip to main content
SpringerLink
Log in

More Stubborn Set Methods for Process Algebras

  • Chapter
  • First Online:
Concurrency, Security, and Puzzles

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10160))

Abstract

Six stubborn set methods for computing reduced labelled transition systems are presented. Two of them preserve the traces, and one is tailored for on-the-fly verification of safety properties. The rest preserve the tree failures, fair testing equivalence, or the divergence traces. Two methods are entirely new, the ideas of three are recent and the adaptation to the process-algebraic setting with non-deterministic actions is new, and one is recent but slightly generalized. Most of the methods address problems in earlier solutions to the so-called ignoring problem. The correctness of each method is proven, and efficient implementation is discussed.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. MIT Press, Cambridge (1999). 314 pages

    Google Scholar 

  2. Evangelista, S., Pajault, C.: Solving the ignoring problem for partial order reduction. Softw. Tools Technol. Transfer 12(2), 155–170 (2010)

    Article  Google Scholar 

  3. Eve, J., Kurki-Suonio, R.: On computing the transitive closure of a relation. Acta Informatica 8(4), 303–314 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  4. Gerth, R., Kuiper, R., Peled, D., Penczek, W.: A partial order approach to branching time logic model checking. In: Proceedings of Third Israel Symposium on the Theory of Computing and Systems, pp. 130–139. IEEE (1995)

    Google Scholar 

  5. Godefroid, P.: Partial-Order Methods for the Verification of Concurrent Systems: An Approach to the State-Explosion Problem. LNCS, vol. 1032. Springer, Heidelberg (1996)

    MATH  Google Scholar 

  6. Hansen, H., Valmari, A.: Safety property-driven stubborn sets. In: Larsen, K.G., Potapov, I., Srba, J. (eds.) RP 2016. LNCS, vol. 9899, pp. 90–103. Springer, Heidelberg (2016). doi:10.1007/978-3-319-45994-3_7

    Chapter  Google Scholar 

  7. Milner, R.: Communication and Concurrency. Prentice-Hall, Englewood Cliffs (1989)

    MATH  Google Scholar 

  8. Peled, D.: Partial order reduction: linear and branching temporal logics and process algebras. In: Peled, D., Pratt, V., Holzmann, G. (eds.) Proceedings of a DIMACS Workshop on Partial Order Methods in Verification. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 29, pp. 233–257. American Mathematical Society (1997)

    Google Scholar 

  9. Peled, D., Valmari, A., Kokkarinen, I.: Relaxed visibility enhances partial order reduction. Formal Meth. Syst. Des. 19, 275–289 (2001)

    Article  MATH  Google Scholar 

  10. Rensink, A., Vogler, W.: Fair testing. Inf. Comput. 205(2), 125–198 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  11. Roscoe, A.W.: Understanding Concurrent Systems. Springer, Heidelberg (2010)

    Book  MATH  Google Scholar 

  12. Tarjan, R.E.: Depth-first search and linear graph algorithms. SIAM J. Comput. 1(2), 146–160 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  13. Valmari, A.: Error detection by reduced reachability graph generation. In: Proceedings of the 9th European Workshop on Application and Theory of Petri Nets, pp. 95–122 (1988)

    Google Scholar 

  14. Valmari, A.: Alleviating state explosion during verification of behavioural equivalence. Department of Computer Science, University of Helsinki, Report A-1992-4, Helsinki, Finland (1992). 57 pages

    Google Scholar 

  15. Valmari, A.: Stubborn set methods for process algebras. In: Peled, D., Pratt, V., Holzmann, G. (eds.) Proceedings of a DIMACS Workshop on Partial Order Methods in Verification. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 29, pp. 213–231. American Mathematical Society (1997)

    Google Scholar 

  16. Valmari, A.: Stop it, and be stubborn! In: Haar, S., Meyer, R. (eds.) 15th International Conference on Application of Concurrency to System Design, pp. 10–19. IEEE Computer Society (2015). doi:10.1109/ACSD.2015.14

  17. Valmari, A.: A state space tool for concurrent system models expressed in C++. In: Nummenmaa, J., Sievi-Korte, O., Mäkinen, E. (eds.) SPLST 2015, Symposium on Programming Languages and Software Tools. CEUR Workshop Proceedings, vol. 1525, pp. 91–105 (2015)

    Google Scholar 

  18. Valmari, A.: The congruences below fair testing with initial stability. In: Desel, J., Yakovlev, A. (eds.) 16th International Conference on Application of Concurrency to System Design (The proceedings to officially appear when IEEE Computer Society condescends to publish it. Based on earlier experience, it may take more than half a year)

    Google Scholar 

  19. Valmari, A., Hansen, H.: Stubborn set intuition explained. In: Cabac, L., Kristensen, L.M., Rölke, H. (eds.) Proceedings of the International Workshop on Petri Nets and Software Engineering 2016. CEUR Workshop Proceedings, vol. 1591, pp. 213–232 (2016)

    Google Scholar 

  20. Valmari, A., Vogler, W.: Fair testing and stubborn sets. In: Bošnački, D., Wijs, A. (eds.) SPIN 2016. LNCS, vol. 9641, pp. 225–243. Springer International Publishing, Cham (2016). doi:10.1007/978-3-319-32582-8_16

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Tampere University of Technology, P.O. Box 553, FI-33101, Tampere, Finland

    Antti Valmari

Authors
  1. Antti Valmari
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Antti Valmari .

Editor information

Editors and Affiliations

  1. University of Oxford, Oxford, United Kingdom

    Thomas Gibson-Robinson

  2. University of Oxford, Oxford, United Kingdom

    Philippa Hopcroft

  3. University of Warwick, Coventry, United Kingdom

    Ranko Lazić

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Valmari, A. (2017). More Stubborn Set Methods for Process Algebras. In: Gibson-Robinson, T., Hopcroft, P., Lazić, R. (eds) Concurrency, Security, and Puzzles. Lecture Notes in Computer Science(), vol 10160. Springer, Cham. https://doi.org/10.1007/978-3-319-51046-0_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-51046-0_13

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-51045-3

  • Online ISBN: 978-3-319-51046-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation