Skip to main content
SpringerLink
Log in
SpringerLink
Log in

Model Checking Parameterized Systems

  • Chapter
  • First Online:
Handbook of Model Checking

Abstract

We consider the model-checking problem for a particular class of parameterized systems: systems that consist of arbitrary numbers of components. The task is to show correctness regardless of the number of components. The term parameterized refers to the fact that the size of the system is a parameter of the verification problem. Examples of parameterized systems include mutual exclusion algorithms, bus protocols, networking protocols, cache coherence protocols, web services, and sensor networks. In this chapter, we will give four examples of techniques that have been used (among many others) for the verification of parameterized systems.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abadi, M., Lamport, L.: Composing specifications. In: ACM Transactions on Programming Languages and Systems. ACM, New York (1993)

    Google Scholar 

  2. Abdulla, P.A., Cerans, K., Jonsson, B., Tsay, Y.K.: General decidability theorems for infinite-state systems. In: Symp. on Logic in Computer Science (LICS), pp. 313–321. IEEE, Piscataway (1996)

    Google Scholar 

  3. Abdulla, P.A., Delzanno, G., Henda, N.B., Rezine, A.: Regular model checking without transducers (on efficient verification of parameterized systems). In: Grumberg, O., Huth, M. (eds.) Intl. Conf. on Tools and Algorithms for the Construction and Analysis of Systems (TACAS). LNCS, vol. 4424, pp. 721–736. Springer, Heidelberg (2007)

    MATH  Google Scholar 

  4. Abdulla, P.A., Haziza, F., Hol’ik, L.: All for the price of few (parameterized verification through view abstraction). In: Giacobazzi, R., Berdine, J., Mastroeni, I. (eds.) Intl. Conf. on Verification, Model Checking and Abstract Interpretation (VMCAI). LNCS, vol. 7737, pp. 476–495. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  5. Abdulla, P.A., Jonsson, B., Nilsson, M., d’Orso, J.: Regular model checking made simple and efficient. In: Brim, L., Jancar, P., Kretínský, M., Kucera, A. (eds.) Intl. Conf. on Concurrency Theory (CONCUR). LNCS, vol. 2421, pp. 116–130. Springer, Heidelberg (2002)

    Google Scholar 

  6. Abdulla, P.A., Jonsson, B., Nilsson, M., d’Orso, J., Saksena, M.: Regular model checking for LTL(MSO). In: Alur, R., Peled, D.A. (eds.) Intl. Conf. on Computer-Aided Verification (CAV). LNCS, vol. 3114, pp. 348–360. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  7. Abdulla, P.A., Jonsson, B., Nilsson, M., Saksena, M.: A survey of regular model checking. In: Intl. Conf. on Concurrency Theory (CONCUR). LNCS, vol. 3170, pp. 35–48. Springer, Heidelberg (2004)

    Google Scholar 

  8. Apt, K.R., Kozen, D.: Limits for automatic verification of finite-state concurrent systems. Inf. Process. Lett. 22(6), 307–309 (1986)

    Article  MathSciNet  Google Scholar 

  9. Arons, T., Pnueli, A., Ruah, S., Xu, J., Zuck, L.D.: Parameterized verification with automatically computed inductive assertions. In: Berry, G., Comon, H., Finkel, A. (eds.) Intl. Conf. on Computer-Aided Verification (CAV). LNCS, vol. 2102, pp. 221–234. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  10. Baukus, K., Lakhnech, Y., Stahl, K.: Parameterized verification of a cache coherence protocol: safety and liveness. In: Cortesi, A. (ed.) Intl. Conf. on Verification, Model Checking and Abstract Interpretation (VMCAI). LNCS, vol. 2294, pp. 317–330. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  11. Bhattacharya, R., German, S.M., Gopalakrishnan, G.: Exploiting symmetry and transactions for partial order reduction of rule based specifications. In: Valmari, A. (ed.) Intl. Symposium on Model Checking of Software (SPIN). LNCS, vol. 3925. Springer, Heidelberg (2006)

    Google Scholar 

  12. Bloem, R., Jacobs, S., Khalimov, A., Konnov, I., Rubin, S., Veith, H., Widder, J.: Decidability of Parameterized Verification. Synthesis Lectures on Distributed Computing Theory. Morgan & Claypool, San Rafael (2015)

    Google Scholar 

  13. Boigelot, B., Legay, A., Wolper, P.: Iterating transducers in the large (extended abstract). In: Hunt, W.A. Jr., Somenzi, F. (eds.) Intl. Conf. on Computer-Aided Verification (CAV). LNCS, vol. 2725, pp. 223–235. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  14. Boigelot, B., Legay, A., Wolper, P.: Omega-regular model checking. In: Jensen, K., Podelski, A. (eds.) Intl. Conf. on Tools and Algorithms for the Construction and Analysis of Systems (TACAS). LNCS, vol. 2988, pp. 561–575. Springer, Heidelberg (2004)

    Google Scholar 

  15. Bouajjani, A., Habermehl, P., Rogalewicz, A., Vojnar, T.: Abstract regular (tree) model checking. Int. J. Softw. Tools Technol. Transf. 14(2), 167–191 (2012)

    Article  Google Scholar 

  16. Bouajjani, A., Habermehl, P., Vojnar, T.: Abstract regular model checking. In: Alur, R., Peled, D.A. (eds.) Intl. Conf. on Computer-Aided Verification (CAV). LNCS, vol. 3114, pp. 372–386. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  17. Bouajjani, A., Touili, T.: Extrapolating tree transformations. In: Brinksma, E., Larsen, K.G. (eds.) Intl. Conf. on Computer-Aided Verification (CAV). LNCS, vol. 2404, pp. 539–554. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  18. Browne, M., Clarke, E.M., Grumberg, O.: Reasoning about networks with many identical finite state processes. Inf. Comput. 81(1), 13–31 (1989)

    Article  MathSciNet  Google Scholar 

  19. Chen, X., Yang, Y., DeLisi, M., Gopalakrishnan, G., Chou, C.T.: Hierarchical cache coherence protocol verification one level at a time through assume guarantee. In: High Level Design Validation and Test Workshop (HLDVT). IEEE, Piscataway (2007)

    Google Scholar 

  20. Chou, C.T., Mannava, P.K., Park, S.: A simple method for parameterized verification of cache coherence protocols. In: Hu, A.J., Martin, A.K. (eds.) Formal Methods in Computer Aided Design (FMCAD). LNCS, vol. 3312. Springer, Heidelberg (2004)

    Google Scholar 

  21. Clarke, E.M., Grumberg, O., Jha, S.: Verifying parameterized networks using abstraction and regular languages. ACM Trans. Program. Lang. Syst. 19(5), 726–750 (1997)

    Article  Google Scholar 

  22. Clarke, E.M., Jha, S., Enders, R., Filkorn, T.: Exploiting symmetry in temporal logic model checking. Form. Methods Syst. Des. 9(1/2), 77–104 (1996)

    Article  Google Scholar 

  23. Clarke, E.M., Talupur, M., Veith, H.: Environment abstraction for parameterized verification. In: Emerson, E.A., Namjoshi, K.S. (eds.) Intl. Conf. on Verification, Model Checking and Abstract Interpretation (VMCAI). LNCS, vol. 3855, pp. 126–141. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  24. Das, S., Dill, D.L., Park, S.: Experience with predicate abstraction. In: Halbwachs, N., Peled, D.A. (eds.) Intl. Conf. on Computer-Aided Verification (CAV). LNCS, vol. 1633. Springer, Heidelberg (1999)

    Google Scholar 

  25. Delzanno, G.: Automatic verification of parameterized cache coherence protocols. In: Emerson, E.A., Sistla, A.P. (eds.) Intl. Conf. on Computer-Aided Verification (CAV). LNCS, vol. 1855, pp. 53–68. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  26. Delzanno, G.: Verification of consistency protocols via infinite-state symbolic model checking. In: Bolognesi, T., Latella, D. (eds.) Formal Methods for Distributed System Development (FORTE), pp. 171–186. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  27. Delzanno, G., Sangnier, A., Zavattaro, G.: Parameterized verification of ad hoc networks. In: Gastin, P., Laroussinie, F. (eds.) Intl. Conf. on Concurrency Theory (CONCUR). LNCS, vol. 6269, pp. 313–327. Springer, Heidelberg (2010)

    Google Scholar 

  28. Dickson, L.E.: Finiteness of the odd perfect and primitive abundant numbers with \(n\) distinct prime factors. Am. J. Math. 35, 413–422 (1913)

    Article  MathSciNet  Google Scholar 

  29. Emerson, E.A., Kahlon, V.: Reducing model checking of the many to the few. In: Intl. Conf. on Automated Deduction (CADE). LNCS, vol. 1831, pp. 236–254. Springer, Heidelberg (2000)

    Google Scholar 

  30. Emerson, E.A., Kahlon, V.: Exact and efficient verification of parameterized cache coherence protocols. In: Geist, D., Tronci, E. (eds.) Correct Hardware Design and Verification Methods (CHARME). LNCS, vol. 2860, pp. 247–262. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  31. Emerson, E.A., Kahlon, V.: Model checking guarded protocols. In: Symp. on Logic in Computer Science (LICS), pp. 361–370. IEEE, Piscataway (2003)

    Google Scholar 

  32. Emerson, E.A., Kahlon, V.: Rapid parameterized model checking of snoopy cache coherence protocols. In: Garavel, H., Hatcliff, J. (eds.) Intl. Conf. on Tools and Algorithms for the Construction and Analysis of Systems (TACAS). LNCS, vol. 2619, pp. 144–159. Springer, Heidelberg (2003)

    MATH  Google Scholar 

  33. Emerson, E.A., Namjoshi, K.S.: Reasoning about rings. In: Cytron, R.K., Lee, P. (eds.) Symp. on Principles of Programming Languages (POPL), pp. 85–94. ACM, New York (1995)

    Google Scholar 

  34. Emerson, E.A., Namjoshi, K.S.: Automatic verification of parameterized synchronous systems. In: Alur, R., Henzinger, T.A. (eds.) Intl. Conf. on Computer-Aided Verification (CAV). LNCS, vol. 1102, pp. 87–98. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  35. Emerson, E.A., Sistla, A.P.: Symmetry and model checking. Form. Methods Syst. Des. 9(1/2), 105–131 (1996)

    Article  Google Scholar 

  36. Esparza, J., Finkel, A., Mayr, R.: On the verification of broadcast protocols. In: Symp. on Logic in Computer Science (LICS), pp. 352–359. IEEE, Piscataway (1999)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  38. German, S.M., Sistla, A.P.: Reasoning about systems with many processes. J. ACM 39(3), 675–735 (1992)

    Article  MathSciNet  Google Scholar 

  39. Henriksen, J.G., Jensen, J.L., Jørgensen, M.E., Klarlund, N., Paige, R., Rauhe, T., Sandholm, A.: Mona: monadic second-order logic in practice. In: Brinksma, E., Cleaveland, R., Larsen, K.G., Margaria, T., Steffen, B. (eds.) Intl. Conf. on Tools and Algorithms for the Construction and Analysis of Systems (TACAS). LNCS, vol. 1019, pp. 89–110. Springer, Heidelberg (1995)

    Google Scholar 

  40. Higman, G.: Ordering by divisibility in abstract algebras. Proc. London Math. Soc. (3) 2(7) (1952)

    Google Scholar 

  41. Ip, C.N., Dill, D.L.: Better verification through symmetry. In: Proc. Conf. on Computer Hardware Description Languages and Their Applications, pp. 97–111 (1993)

    Google Scholar 

  42. Ip, C.N., Dill, D.L.: Better verification through symmetry. Form. Methods Syst. Des. 9(1/2), 41–75 (1996)

    Google Scholar 

  43. Karp, R.M., Miller, R.E.: Parallel program schemata. J. Comput. Syst. Sci. 3(2), 147–195 (1969)

    Article  MathSciNet  Google Scholar 

  44. Kelb, P., Margaria, T., Mendler, M., Gsottberger, C.: Mosel: a flexible toolset for monadic second-order logic. In: Brinksma, E. (ed.) Intl. Conf. on Tools and Algorithms for the Construction and Analysis of Systems (TACAS). LNCS, vol. 1217, pp. 183–202. Springer, Heidelberg (1997)

    Google Scholar 

  45. Kesten, Y., Maler, O., Marcus, M., Pnueli, A., Shahar, E.: Symbolic model checking with rich assertional languages. In: Grumberg, O. (ed.) Intl. Conf. on Computer-Aided Verification (CAV). LNCS, vol. 1254, pp. 424–435. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  46. Krstic, S.: Parameterized system verification with guard strengthening and parameter abstraction. In: Automated Verification of Infinite State Systems (2005)

    Google Scholar 

  47. Kurshan, R.P., McMillan, K.: A structural induction theorem for processes. In: Rudnicki, P. (ed.) ACM Symp. on Principles of Distributed Computing (PODC), pp. 239–247. ACM, New York (1989)

    Google Scholar 

  48. Lahiri, S.K., Bryant, R.E.: Indexed predicate discovery for unbounded system verification. In: Alur, R., Peled, D.A. (eds.) Intl. Conf. on Computer-Aided Verification (CAV). LNCS, vol. 3114, pp. 135–147. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  49. Lamport, L.: A new solution of Dijkstra’s concurrent programming problem. Commun. ACM 17(8), 453–455 (1974)

    Article  MathSciNet  Google Scholar 

  50. Lesens, D., Halbwachs, N., Raymond, P.: Automatic verification of parametrized linear networks of processes. In: Boehm, H.-J., Steele, G.L. Jr. (eds.) Symp. on Principles of Programming Languages (POPL), pp. 101–105. ACM, New York (1996)

    Google Scholar 

  51. Maidl, M.: A unifying model checking approach for safety properties of parameterized systems. In: Berry, G., Comon, H., Finkel, A. (eds.) Intl. Conf. on Computer-Aided Verification (CAV). LNCS, vol. 2102, pp. 311–323. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  52. McMillan, K.L.: Verification of an implementation of Tomasulo’s algorithm by compositional model checking. In: Hu, A.J., Vardi, M.Y. (eds.) Intl. Conf. on Computer-Aided Verification (CAV). LNCS, vol. 1427. Springer, Heidelberg (1998)

    Google Scholar 

  53. McMillan, K.L.: Verification of infinite state systems by compositional model checking. In: Pierre, L., Kropf, T. (eds.) Correct Hardware Design and Verification Methods (CHARME). LNCS, vol. 1703. Springer, Heidelberg (1999)

    Google Scholar 

  54. McMillan, K.L.: Parameterized verification of the FLASH cache coherence protocol by compositional model checking. In: Correct Hardware Design and Verification Methods (CHARME). LNCS, vol. 2144, pp. 179–195. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  55. Misra, J., Chandy, K.M.: Proofs of networks of processes. In: IEEE Transactions on Software Engineering, vol. SE-7. IEEE, Piscataway (1981)

    Google Scholar 

  56. O’Leary, J., Talupur, M., Tuttle, M.R.: Protocol Verification using Flows: Parameterized Verification using Message Flows. Formal Methods in Computer Aided Design (FMCAD). IEEE, Piscataway (2009)

    Google Scholar 

  57. Park, S., Dill, D.L.: Verification of flash cache coherence protocol by aggregation of distributed transactions. In: SPAA ’96: Proceedings of the Eighth Annual ACM Symposium on Parallel Algorithms and Architectures, pp. 288–296. ACM, New York (1996)

    Chapter  Google Scholar 

  58. Pnueli, A., Ruah, S., Zuck, L.D.: Automatic deductive verification with invisible invariants. In: Margaria, T., Yi, W. (eds.) Intl. Conf. on Tools and Algorithms for the Construction and Analysis of Systems (TACAS). LNCS, vol. 2031, pp. 82–97. Springer, Heidelberg (2001)

    Google Scholar 

  59. Pnueli, A., Xu, J., Zuck, L.D.: Liveness with (\(0, 1, \infty\))-counter abstraction. In: Brinksma, E., Larsen, K.G. (eds.) Intl. Conf. on Computer-Aided Verification (CAV). LNCS, vol. 2402, pp. 107–122. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  60. Roychoudhury, A., Ramakrishnan, I.V.: Automated inductive verification of parameterized protocols. In: Berry, G., Comon, H., Finkel, A. (eds.) Intl. Conf. on Computer-Aided Verification (CAV). LNCS, vol. 2102, pp. 25–37. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  61. Sethi, D., Talupur, M., Schwartz-Narbonne, D., Malik, S.: Parameterized model checking of fine grained concurrency. In: Donaldson, A.F., Parker, D. (eds.) Intl. Symposium on Model Checking of Software (SPIN). LNCS, vol. 7385. Springer, Heidelberg (2012)

    Google Scholar 

  62. Shtadler, Z., Grumberg, O.: Network grammars, communication behaviors and automatic verification. In: Sifakis, J. (ed.) Workshop on Automatic Verification Methods for Finite State Systems. LNCS, pp. 151–166. Springer, Heidelberg (1989)

    Google Scholar 

  63. Sistla, A.P., Gyuris, V.: Parameterized verification of linear networks using automata as invariants. Form. Asp. Comput. 11, 402–425 (1999)

    Article  Google Scholar 

  64. Suzuki, I.: Proving properties of a ring of finite-state machines. Inf. Process. Lett. 28(4), 213–214 (1988)

    Article  MathSciNet  Google Scholar 

  65. Szymanski, B.K.: A simple solution to Lamport’s concurrent programming problem with linear wait. In: Lenfant, J. (ed.) International Conference on Supercomputing (ICS), pp. 621–626. ACM, New York (1988)

    Google Scholar 

  66. Talupur, M., Krstic, S., O’Leary, J., Tuttle, M.R.: Parametric verification of industrial strength cache coherence protocols. In: Proc. Workshop on Design of Correct Circuits (DCC) (2008)

    Google Scholar 

  67. Talupur, M., Tuttle, M.R.: Going with the flow: parameterized verification using message flows. In: Cimatti, A., Jones, R.B. (eds.) Formal Methods in Computer Aided Design (FMCAD). IEEE, Piscataway (2008)

    Google Scholar 

  68. Topnik, C., Wilhelm, E., Margaria, T., Steffen, B.: jMosel: a stand-alone tool and jABC plugin for M2L(Str). In: Valmari, A. (ed.) Intl. Symposium on Model Checking of Software (SPIN). LNCS, vol. 3925, pp. 293–298. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  69. Touili, T.: Regular model checking using widening techniques. Electron. Notes Theor. Comput. Sci. 50(4), 342–356 (2001)

    Article  Google Scholar 

  70. Wolper, P., Lovinfosse, V.: Verifying properties of large sets of processes with network invariants. In: Sifakis, J. (ed.) Workshop on Automatic Verification Methods for Finite State Systems, pp. 68–81. Springer, Heidelberg (1989)

    Google Scholar 

  71. Zuck, L.D., Pnueli, A.: Model checking and abstraction to the aid of parameterized systems (a survey). Comput. Lang. Syst. Struct. 30(3–4), 139–169 (2004)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Uppsala University, Uppsala, Sweden

    Parosh Aziz Abdulla

  2. University of Illinois, Chicago, IL, USA

    A. Prasad Sistla

  3. Intel’s Strategic CAD Labs, Hillsboro, OR, USA

    Muralidhar Talupur

Authors
  1. Parosh Aziz Abdulla
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Prasad Sistla
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Muralidhar Talupur
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Parosh Aziz Abdulla .

Editor information

Editors and Affiliations

  1. FORE Systems University Professor of Computer Science, Carnegie Mellon University, Pittsburgh, Pennsylvania, USA

    Edmund M. Clarke

  2. Institute of Science and Technology Austria (IST), Klosterneuburg, Austria

    Thomas A. Henzinger

  3. Arbeitsbereich Formal Methods in Systems Engineering, Technische Universität Wien, Wien, Austria

    Helmut Veith

  4. Institut f. Angewandte Informationsverarbeitung und Kommunikationstechnologie (IAIK), Technische Universität Graz, Graz, Austria

    Roderick Bloem

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Abdulla, P.A., Sistla, A.P., Talupur, M. (2018). Model Checking Parameterized Systems. In: Clarke, E., Henzinger, T., Veith, H., Bloem, R. (eds) Handbook of Model Checking. Springer, Cham. https://doi.org/10.1007/978-3-319-10575-8_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-10575-8_21

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10574-1

  • Online ISBN: 978-3-319-10575-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation