Skip to main content
SpringerLink
Log in

Reversal-Bounded Counter Machines Revisited

  • Conference paper
Mathematical Foundations of Computer Science 2008 (MFCS 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5162))

Abstract

We extend the class of reversal-bounded counter machines by authorizing a finite number of alternations between increasing and decreasing mode over a given bound. We prove that extended reversal-bounded counter machines also have effective semi-linear reachability sets. We also prove that the property of being reversal-bounded is undecidable in general even when we fix the bound, whereas this problem becomes decidable when considering Vector Addition System with States.

Partly supported by project AVERISS (ANR-06-SETIN-001).

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Annichini, A., Bouajjani, A., Sighireanu, M.: TReX: A tool for reachability analysis of complex systems. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 368–372. Springer, Heidelberg (2001)

    Google Scholar 

  2. Araki, T., Kasami, T.: Decidable problems on the strong connectivity of Petri net reachability sets. Theor. Comput. Sci. 4(1), 99–119 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bardin, S., Leroux, J., Point, G.: FAST extended release. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 63–66. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  4. Ibarra, O.H., Dang, Z., San Pietro, P.: Liveness Verification of Reversal-Bounded Multicounter Machines with a Free Counter. In: Hariharan, R., Mukund, M., Vinay, V. (eds.) FSTTCS 2001. LNCS, vol. 2245, pp. 132–143. Springer, Heidelberg (2001)

    Google Scholar 

  5. Esparza, J.: Petri nets, commutative context-free grammars, and basic parallel processes. Fundam. Inform. 31(1), 13–25 (1997)

    MATH  MathSciNet  Google Scholar 

  6. Finkel, A., Leroux, J.: How to compose Presburger-accelerations: Applications to broadcast protocols. In: Agrawal, M., Seth, A.K. (eds.) FSTTCS 2002. LNCS, vol. 2556, pp. 145–156. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  7. Finkel, A., Sangnier, A.: Reversal-bounded counter machines revisited. Research report, Laboratoire Specification et Verification, ENS Cachan (2008)

    Google Scholar 

  8. Higman, G.: Ordering by divisibility in abstract algebras. Proc. London Math. Soc (3) 2, 326–336 (1952)

    Article  MATH  MathSciNet  Google Scholar 

  9. Hopcroft, J.E., Pansiot, J.-J.: On the reachability problem for 5-dimensional vector addition systems. Theor. Comput. Sci. 8, 135–159 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  10. Ibarra, O.H.: Reversal-bounded multicounter machines and their decision problems. J. ACM 25(1), 116–133 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  11. Ibarra, O.H., Su, J., Dang, Z., Bultan, T., Kemmerer, R.A.: Counter machines and verification problems. Theor. Comput. Sci. 289(1), 165–189 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  12. Jantzen, M.: Complexity of place/transition nets. In: APN 1986. LNCS, vol. 254, pp. 413–434. Springer, Heidelberg (1987)

    Google Scholar 

  13. Karp, R.M., Miller, R.E.: Parallel program schemata: A mathematical model for parallel computation. In: FOCS 1967, pp. 55–61. IEEE Computer Society Press, Los Alamitos (1967)

    Google Scholar 

  14. Kosaraju, S.R.: Decidability of reachability in vector addition systems (preliminary version). In: STOC 1982, pp. 267–281. ACM Press, New York (1982)

    Chapter  Google Scholar 

  15. Landweber, L.H., Robertson, E.L.: Properties of conflict-free and persistent Petri nets. J. ACM 25(3), 352–364 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  16. Homepage of LASH, http://www.montefiore.ulg.ac.be/~boigelot/research/lash

  17. Leroux, J., Sutre, G.: Flat counter almost everywhere! In: Peled, D.A., Tsay, Y.-K. (eds.) ATVA 2005. LNCS, vol. 3707, pp. 474–488. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  18. Mayr, E.W.: Persistence of vector replacement systems is decidable. Acta Inf. 15, 309–318 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  19. Mayr, E.W.: An algorithm for the general Petri net reachability problem. SIAM J. Comput. 13(3), 441–460 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  20. Minsky, M.L.: Computation: finite and infinite machines. Prentice-Hall, Inc., Upper Saddle River, NJ, USA (1967)

    MATH  Google Scholar 

  21. Valk, R., Vidal-Naquet, G.: Petri nets and regular languages. J. Comput. Syst. Sci. 23(3), 299–325 (1981)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LSV, ENS Cachan, CNRS,  

    Alain Finkel & Arnaud Sangnier

  2. EDF R&D, 61 av. du pdt Wilson, 94230, Cachan, France

    Arnaud Sangnier

Authors
  1. Alain Finkel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Arnaud Sangnier
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Edward Ochmański Jerzy Tyszkiewicz

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Finkel, A., Sangnier, A. (2008). Reversal-Bounded Counter Machines Revisited. In: Ochmański, E., Tyszkiewicz, J. (eds) Mathematical Foundations of Computer Science 2008. MFCS 2008. Lecture Notes in Computer Science, vol 5162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85238-4_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-85238-4_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85237-7

  • Online ISBN: 978-3-540-85238-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation