Skip to main content
SpringerLink
Log in

Handling Infinitely Branching WSTS

  • Conference paper
Book cover Automata, Languages, and Programming (ICALP 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8573))

Included in the following conference series:

Abstract

Most decidability results concerning well-structured transition systems apply to the finitely branching variant. Yet some models (inserting automata, ω-Petri nets, ...) are naturally infinitely branching. Here we develop tools to handle infinitely branching WSTS by exploiting the crucial property that in the (ideal) completion of a well-quasi-ordered set, downward-closed sets are finite unions of ideals. Then, using these tools, we derive decidability results and we delineate the undecidability frontier in the case of the termination, the control-state maintainability and the coverability problems. Coverability and boundedness under new effectivity conditions are shown decidable.

Supported by the French Agence Nationale de la Recherche, REACHARD (grant ANR-11-BS02-001), by the Fonds québécois de la recherche sur la nature et les technologies, by the Natural Sciences and Engineering Research Council of Canada and by the “Chaire DIGITEO, ENS Cachan - École Polytechnique”.

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 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. Abdulla, P.A., Cerans, K., Jonsson, B., Tsay, Y.K.: General decidability theorems for infinite-state systems. In: LICS, pp. 313–321 (1996)

    Google Scholar 

  2. Abdulla, P.A., Cerans, K., Jonsson, B., Tsay, Y.K.: Algorithmic analysis of programs with well quasi-ordered domains. Inf. Comput. 160(1-2), 109–127 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  3. Abramsky, S., Jung, A.: Domain theory. In: Handbook of Logic in Comp. Sci., vol. 3, pp. 1–168. Oxford University Press (1994)

    Google Scholar 

  4. Bertrand, N., Delzanno, G., König, B., Sangnier, A., Stückrath, J.: On the decidability status of reachability and coverability in graph transformation systems. In: RTA, pp. 101–116 (2012)

    Google Scholar 

  5. Bertrand, N., Schnoebelen, P.: Computable fixpoints in well-structured symbolic model checking. Formal Methods in System Design 43(2), 233–267 (2013)

    Article  MATH  Google Scholar 

  6. Bouyer, P., Markey, N., Ouaknine, J., Schnoebelen, P., Worrell, J.: On termination and invariance for faulty channel systems. FAC 24(4-6), 595–607 (2012)

    MATH  MathSciNet  Google Scholar 

  7. Cécé, G., Finkel, A., Iyer, S.P.: Unreliable channels are easier to verify than perfect channels. Inf. Comput. 124(1), 20–31 (1996)

    Article  MATH  Google Scholar 

  8. Dufourd, C., Finkel, A., Schnoebelen, P.: Reset nets between decidability and undecidability. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 103–115. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  9. Dufourd, C., Jančar, P., Schnoebelen, P.: Boundedness of reset P/T nets. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 301–310. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  10. Esparza, J., Finkel, A., Mayr, R.: On the verification of broadcast protocols. In: LICS, pp. 352–359 (1999)

    Google Scholar 

  11. Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere! Theoret. Comput. Sci. 256(1–2), 63–92 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  12. Finkel, A.: Reduction and covering of infinite reachability trees. Information and Computation 89(2), 144–179 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  13. Finkel, A., Goubault-Larrecq, J.: Forward analysis for WSTS, part I: Completions. In: STACS, pp. 433–444 (2009)

    Google Scholar 

  14. Finkel, A., Goubault-Larrecq, J.: Forward analysis for WSTS, Part II: Complete WSTS. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009, Part II. LNCS, vol. 5556, pp. 188–199. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  15. Finkel, A., McKenzie, P., Picaronny, C.: A well-structured framework for analysing Petri net extensions. Information and Computation 195(1-2), 1–29 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  16. Ganty, P., Raskin, J.-F., Van Begin, L.: A complete abstract interpretation framework for coverability properties of WSTS. In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 49–64. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  17. Geeraerts, G., Heußner, A., Praveen, M., Raskin, J.F.: ω-Petri nets. In: Petri Nets, pp. 49–69 (2013)

    Google Scholar 

  18. Geeraerts, G., Raskin, J.F., Begin, L.V.: Expand, enlarge and check: New algorithms for the coverability problem of WSTS. JCSS 72(1), 180–203 (2006)

    Article  MATH  Google Scholar 

  19. Goubault-Larrecq, J., Schnoebelen, P.: Personal communication (October 2013)

    Google Scholar 

  20. Jancar, P.: A note on well quasi-orderings for powersets. Inf. Process. Lett. 72(5-6), 155–160 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  21. Kaiser, A., Kroening, D., Wahl, T.: Efficient coverability analysis by proof minimization. In: Koutny, M., Ulidowski, I. (eds.) CONCUR 2012. LNCS, vol. 7454, pp. 500–515. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  22. König, B., Stückrath, J.: Well-structured graph transformation systems with negative application conditions. In: Ehrig, H., Engels, G., Kreowski, H.-J., Rozenberg, G. (eds.) ICGT 2012. LNCS, vol. 7562, pp. 81–95. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  23. Pachl, J.K.: Reachability problems for communicating finite state machines. Technical Report CS-82-12, University of Waterloo (1982)

    Google Scholar 

  24. Schmitz, S., Schnoebelen, P.: Multiply-recursive upper bounds with Higman’s lemma. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 441–452. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  25. Schmitz, S., Schnoebelen, P.: The power of well-structured systems. In: D’Argenio, P.R., Melgratti, H. (eds.) CONCUR 2013 – Concurrency Theory. LNCS, vol. 8052, pp. 5–24. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  26. Wies, T., Zufferey, D., Henzinger, T.A.: Forward analysis of depth-bounded processes. In: Ong, L. (ed.) FOSSACS 2010. LNCS, vol. 6014, pp. 94–108. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  27. Zufferey, D., Wies, T., Henzinger, T.A.: Ideal abstractions for well-structured transition systems. In: Kuncak, V., Rybalchenko, A. (eds.) VMCAI 2012. LNCS, vol. 7148, pp. 445–460. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Université de Montréal, Canada

    Michael Blondin & Pierre McKenzie

  2. ENS Cachan, France

    Michael Blondin, Alain Finkel & Pierre McKenzie

Authors
  1. Michael Blondin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alain Finkel
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pierre McKenzie
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Informatik, Technische Universität München, Boltzmannstrasse 3, 85748, München, Germany

    Javier Esparza

  2. LIAFA, Université Paris Diderot-Paris 7, Case 7014, 75205, Paris Cedex 13, France

    Pierre Fraigniaud

  3. IT University of Copenhagen, Rued Langgaards Vej 7, 2300, Copenhagen, Denmark

    Thore Husfeldt

  4. Department Computer Science, University of Oxford, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK,

    Elias Koutsoupias

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Blondin, M., Finkel, A., McKenzie, P. (2014). Handling Infinitely Branching WSTS. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds) Automata, Languages, and Programming. ICALP 2014. Lecture Notes in Computer Science, vol 8573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43951-7_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-43951-7_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-43950-0

  • Online ISBN: 978-3-662-43951-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation