Skip to main content

Applying Step Coverability Trees to Communicating Component-Based Systems

  • Conference paper
Book cover Fundamentals of Software Engineering (FSEN 2009)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 5961))

Included in the following conference series:

Abstract

Like reachability, coverability is an important tool for verifying behavioural properties of dynamic systems. When a system is modelled as a Petri net, the classical Karp-Miller coverability tree construction can be used to decide questions related to the (required) capacity of local states. Correctness (termination) of the construction is based on a monotonicity property: more resources available implies more behaviour possible. Here we discuss a modification of the coverability tree construction allowing one to deal with concurrent occurrences of actions (steps) and to extend the notion of coverability to a dynamic action-based notion (thus viewing bandwidth as a resource). We are in particular interested in component-based systems in which steps are subject to additional constraints like (local) synchronicity or maximal concurrency. In general the behaviour of such systems is not monotonous and hence new termination criteria (depending on the step semantics) are needed. We here investigate marked graphs, a Petri net model for systems consisting of concurrent components communicating via buffers.

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

Access this chapter

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Agerwala, T.: A Complete Model for Representing the Coordination of Asynchronous Processes. In: Hopkins Comp. Research Rep., vol. 32. Johns Hopkins Univ. (1974)

    Google Scholar 

  2. Baeten, J.C.M., Weijland, W.P.: Process algebra. Cambridge Tracts in Theoretical Computer Science, vol. 18. Cambridge University Press, Cambridge (1990)

    Google Scholar 

  3. Busi, N.: Analysis Issues in Petri Nets with Inhibitor Arcs. Theoretical Computer Science 275, 127–177 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  4. Commoner, F., Holt, A.W., Even, S., Pnueli, A.: Marked Directed Graphs. J. Comput. Syst. Sci. 5, 511–523 (1971)

    MATH  MathSciNet  Google Scholar 

  5. Darondeau, P., Genest, B., Thiagarajan, P.S., Yang, S.: Quasi-Static Scheduling of Communicating Tasks. In: van Breugel, F., Chechik, M. (eds.) CONCUR 2008. LNCS, vol. 5201, pp. 310–324. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  6. Desel, J., Esparza, J.: Free Choice Nets. Cambridge University Press, Cambridge (1995)

    Book  MATH  Google Scholar 

  7. Desel, J., Reisig, W.: Place/Transition Petri Nets. In: [20], pp. 122–173

    Google Scholar 

  8. Esparza, J., Nielsen, M.: Decidability Issues for Petri Nets: A Survey. J. of Inf. Processing and Cybernetics 30, 143–160 (1994)

    MATH  Google Scholar 

  9. Ghamarian, A.H., Geilen, M.C.W., Basten, T., Theelen, B.D., Mousavi, M.R., Stuijk, S.: Liveness and Boundedness of Synchronous Data Flow Graphs. In: FMCAD 2006, pp. 12–16 (2006)

    Google Scholar 

  10. Hack, M.: Decision Problems for Petri Nets and Vector Addition Systems. Technical Memo 59, Project MAC, MIT (1975)

    Google Scholar 

  11. Hoare, C.A.R.: Communicating Sequential Processes. Prentice-Hall, Englewood Cliffs (1985)

    MATH  Google Scholar 

  12. Karp, R.M., Miller, R.E.: Parallel Program Schemata. J. Comput. Syst. Sci. 3, 147–195 (1969)

    MATH  MathSciNet  Google Scholar 

  13. Kleijn, J., Koutny, M.: Steps and Coverability in Inhibitor Nets. In: Lodaya, K., Mukund, M., Ramanujam, R. (eds.) Perspectives in Concurrency Theory, pp. 264–295. Universities Press, Hyderabad (2008)

    Google Scholar 

  14. Kleijn, J., Koutny, M., Rozenberg, G.: Process Semantics for Membrane Systems. J. of Aut., Lang. and Comb. 11, 321–340 (2006)

    MATH  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  16. Milner, R., Parrow, J., Walker, D.: A Calculus of Mobile Processes. Inf. and Comp. 100, 1–77 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  17. Peterson, J.L.: Petri Net Theory and the Modeling of Systems. Prentice-Hall, Englewood Cliffs (1981)

    Google Scholar 

  18. Petri, C.A.: Fundamentals of a Theory of Asynchronous Information Flow. In: IFIP Congress 1962, pp. 386–390. North Holland, Amsterdam (1962)

    Google Scholar 

  19. Rozenberg, G., Engelfriet, J.: Elementary Net Systems. In: [20], 12–121

    Google Scholar 

  20. Reisig, W., Rozenberg, G. (eds.): APN 1998. LNCS, vol. 1491. Springer, Heidelberg (1998)

    MATH  Google Scholar 

  21. Rozenberg, G., Thiagarajan, P.S.: Petri Nets: Basic Notions, Structure, Behaviour. In: Rozenberg, G., de Bakker, J.W., de Roever, W.-P. (eds.) Current Trends in Concurrency. LNCS, vol. 224, pp. 585–668. Springer, Heidelberg (1986)

    Chapter  Google Scholar 

  22. Valmari, A.: The State Explosion Problem. In: [20], 429–528

    Google Scholar 

  23. Wimmel, H.: Entscheidbarkeitsfragen bei Petri Netzen. Habilitation (2007)

    Google Scholar 

  24. Yoeli, M.: Specification and Verification of Asynchronous Circuits using Marked Graphs. In: Rozenberg, G. (ed.) APN 1987. LNCS, vol. 266, pp. 605–622. Springer, Heidelberg (1987)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kleijn, J., Koutny, M. (2010). Applying Step Coverability Trees to Communicating Component-Based Systems . In: Arbab, F., Sirjani, M. (eds) Fundamentals of Software Engineering. FSEN 2009. Lecture Notes in Computer Science, vol 5961. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11623-0_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-11623-0_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11622-3

  • Online ISBN: 978-3-642-11623-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics