Skip to main content
SpringerLink
Log in

The Complexity of Reversal-Bounded Model-Checking

  • Conference paper
Frontiers of Combining Systems (FroCoS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6989))

Included in the following conference series:

Abstract

We study model-checking problems on counter systems when guards are quantifier-free Presburger formulae, the specification languages are LTL-like dialects with arithmetical constraints and the runs are restricted to reversal-bounded ones. We introduce a generalization of reversal-boundedness and we show the NExpTime-completeness of the reversal-bounded model-checking problem as well as for related reversalbounded reachability problems. As a by-product, we show the effective Presburger definability for sets of configurations for which there is a reversal-bounded run verifying a given temporal formula. Our results generalize existing results about reversal-bounded counter automata and provides a uniform and more general framework.

Work supported by Agence Nationale de la Recherche, grant ANR-06-SETIN-001 and by the European Commission, Project 227977-SMScom.

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 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.99
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. Alur, R., Henzinger, T.: A really temporal logic. In: FOCS 1989, pp. 164–169. IEEE, Los Alamitos (1989)

    Google Scholar 

  2. Barrett, C., Tinelli, C.: CVC3. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 298–302. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  3. Becker, B., Dax, C., Eisinger, J., Klaedtke, F.: LIRA: Handling Constraints of Linear Arithmetics over the Integers and the Reals. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 307–310. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  4. Bersani, M., Demri, S.: The complexity of reversal-bounded model checking. Tech. Rep. LSV-11-10, LSV, ENS Cachan, France (May 2011)

    Google Scholar 

  5. Bersani, M., Frigeri, A., Morzenti, A., Pradella, M., Rossi, M., San Pietro, P.: Bounded reachability for temporal logic over constraint systems. In: TIME 2010, pp. 43–50. IEEE, Los Alamitos (2010)

    Google Scholar 

  6. Biere, A., Cimatti, A., Clarke, E.M., Strichman, O., Zhu, Y.: Bounded model checking. Advances in Computers 58, 118–149 (2003)

    Google Scholar 

  7. Borosh, I., Treybig, L.: Bounds on positive integral solutions of linear diophantine equations. Proocedings of The American Mathematical Society 55, 299–304 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  8. Bouajjani, A., Echahed, R., Habermehl, P.: On the verification problem of nonregular properties for nonregular processes. In: LICS 1995, pp. 123–133 (1995)

    Google Scholar 

  9. Čerāns, K.: Deciding properties of integral relational automata. In: Shamir, E., Abiteboul, S. (eds.) ICALP 1994. LNCS, vol. 820, pp. 35–46. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  10. Dang, Z., Ibarra, O., 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)

    Chapter  Google Scholar 

  11. Demri, S.: On Selective Unboundedness of VASS. In: INFINITY 2010. EPTCS, vol. 39, pp. 1–15 (2010)

    Google Scholar 

  12. Esparza, J.: Decidability and complexity of Petri net problems — an introduction. In: Reisig, W., Rozenberg, G. (eds.) APN 1998. LNCS, vol. 1491, pp. 374–428. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  13. Finkel, A., Sangnier, A.: Reversal-bounded counter machines revisited. In: Ochmański, E., Tyszkiewicz, J. (eds.) MFCS 2008. LNCS, vol. 5162, pp. 323–334. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  14. Gurari, E., Ibarra, O.: The complexity of decision problems for finite-turn multicounter machines. In: Even, S., Kariv, O. (eds.) ICALP 1981. LNCS, vol. 115, pp. 495–505. Springer, Heidelberg (1981)

    Chapter  Google Scholar 

  15. Habermehl, P.: On the complexity of the linear-time mu-calculus for Petri nets. In: Azéma, P., Balbo, G. (eds.) ICATPN 1997. LNCS, vol. 1248, pp. 102–116. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  16. Hague, M., Lin, A.W.: Model checking recursive programs with numeric data types. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 743–759. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  17. Howell, R., Rosier, L.: An analysis of the nonemptiness problem for classes of reversal-bounded multicounter machines. JCSS 34(1), 55–74 (1987)

    MATH  MathSciNet  Google Scholar 

  18. Ibarra, O.H., Bultan, T., Su, J.: Reachability analysis for some models of infinite-state transition systems. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 183–198. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  19. Ibarra, O., Su, J., Dang, Z., Bultan, T., Kemmerer, R.: Counter Machines and Verification Problems. TCS 289(1), 165–189 (2002)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  21. Kopczynski, E., To, A.: Parikh Images of Grammars: Complexity and Applications. In: LICS 2010, pp. 80–89. IEEE, Los Alamitos (2010)

    Google Scholar 

  22. Laroussinie, F., Meyer, A., Petonnet, E.: Counting LTL. In: TIME 2010, pp. 51–58. IEEE, Los Alamitos (2010)

    Google Scholar 

  23. Leroux, J., Point, G.: TaPAS: The Talence Presburger Arithmetic Suite. In: Kowalewski, S., Philippou, A. (eds.) TACAS 2009. LNCS, vol. 5505, pp. 182–185. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  24. Leroux, J., Sutre, G.: Flat counter automata almost everywhere! In: Peled, D.A., Tsay, Y.-K. (eds.) ATVA 2005. LNCS, vol. 3707, pp. 489–503. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  25. Lutz, C.: NEXPTIME-complete description logics with concrete domains. ACM ToCL 5(4), 669–705 (2004)

    Article  MathSciNet  Google Scholar 

  26. de Moura, L., Björner, N.: Z3: An Efficient SMT Solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  27. Papadimitriou, C.: On the complexity of integer programming. JACM 28(4), 765–768 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  28. Presburger, M.: Über die Vollständigkeit eines gewissen Systems der Arithmetik ganzer Zahlen, in welchem die Addition als einzige Operation hervortritt. In: Comptes Rendus du premier congrès de mathématiciens des Pays Slaves, Warszawa, pp. 92–101 (1930)

    Google Scholar 

  29. Qadeer, S., Rehof, J.: Context-bounded model checking of concurrent software. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 93–107. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  30. Rackoff, C.: The covering and boundedness problems for vector addition systems. TCS 6(2), 223–231 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  31. Suzuki, N., Jefferson, D.: Verification Decidability of Presburger Array Programs. JACM 27(1), 191–205 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  32. To, A.: Model Checking Infinite-State Systems: Generic and Specific Approaches. Ph.D. thesis, School of Informatics, University of Edinburgh (2010)

    Google Scholar 

  33. To, A., Libkin, L.: Algorithmic metatheorems for decidable LTL model checking over infinite systems. In: Ong, L. (ed.) FOSSACS 2010. LNCS, vol. 6014, pp. 221–236. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  34. Vardi, M., Wolper, P.: Reasoning about infinite computations. I&C 115, 1–37 (1994)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LSV, ENS Cachan, CNRS, INRIA, France

    Marcello M. Bersani & Stéphane Demri

  2. Politecnico di Milano, Italy

    Marcello M. Bersani

Authors
  1. Marcello M. Bersani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stéphane Demri
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Iowa, USA

    Cesare Tinelli

  2. Max-Planck-Institut für Informatik, Campus E 1.4, 66123, Saarbrücken, Germany

    Viorica Sofronie-Stokkermans

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bersani, M.M., Demri, S. (2011). The Complexity of Reversal-Bounded Model-Checking. In: Tinelli, C., Sofronie-Stokkermans, V. (eds) Frontiers of Combining Systems. FroCoS 2011. Lecture Notes in Computer Science(), vol 6989. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24364-6_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-24364-6_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24363-9

  • Online ISBN: 978-3-642-24364-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation