Skip to main content

Partial-Order Reduction

  • Chapter
  • First Online:
Handbook of Model Checking

Abstract

Partial order reduction methods help reduce the time and space required to automatically verify concurrent asynchronous systems based on commutativity between concurrently executed transitions. We describe partial order reduction for various specification formalisms, such as LTL, CTL, and process algebra.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alur, R., Brayton, R., Henzinger, T., Qadeer, S., Rajamani, S.: Partial order reduction in symbolic state space exploration. In: Grumberg, O. (ed.) Intl. Conf. on Computer-Aided Verification (CAV). LNCS, vol. 1254, pp. 340–351. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  2. Bosnacki, D., Elkind, E., Genest, B., Peled, D.: On commutativity based edge lean search. In: Arge, L., Cachin, C., Jurdzinski, T., Tarlecki, A. (eds.) Intl. Colloquium on Automata, Languages and Programming (ICALP). LNCS, vol. 4596, pp. 158–170. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  3. Browne, M., Clarke, E., Grumberg, O.: Characterizing finite Kripke structures in propositional temporal logic. Theor. Comput. Sci. 59(1–2), 115–131 (1988)

    Article  MathSciNet  Google Scholar 

  4. Chou, C., Peled, D.: Verifying a model-checking algorithm. In: Margaria, T., Steffen, B. (eds.) Intl. Conf. on Tools and Algorithms for the Construction and Analysis of Systems (TACAS). LNCS, vol. 1055, pp. 241–257. Springer, Heidelberg (1996)

    Google Scholar 

  5. Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (2000)

    Google Scholar 

  6. Courcoubetis, C., Vardi, M., Wolper, P., Yannakakis, M.: Memory-efficient algorithms for the verification of temporal properties. Form. Methods Syst. Des. 1(2–3), 275–288 (1992)

    Article  Google Scholar 

  7. De Nicola, R., Vaandrager, F.: Three logics for branching bisimulation. In: Symp. on Logic in Computer Science, vol. LICS, pp. 118–129. IEEE, Piscataway (1990)

    Google Scholar 

  8. Esparza, J., Heljanko, K.: Unfoldings—a partial-order approach to model checking. EATCS Monographs in Theoretical Computer Science. Springer, Heidelberg (2008)

    MATH  Google Scholar 

  9. Gerth, R., Kuiper, R., Penczek, W., Peled, D.: A partial order approach to branching time logic model checking. In: Israel Symp. on the Theory of Computing and Systems (ISTCS), pp. 130–139. IEEE, Piscataway (1995). Full version in Information and Computation 150(2), 132–152 (1999)

    Google Scholar 

  10. Gerth, R., Peled, D., Vardi, M., Wolper, P.: Simple on-the-fly automatic verification of linear temporal logic. In: Dembinski, P., Sredniawa, M. (eds.) Intl. Symp. on Protocol Specification, Testing and Verification (PSTV). IFIP Conference Proceedings, vol. 38, pp. 3–18. Chapman & Hall, London (1995)

    Google Scholar 

  11. van Glabbeek, R., Weijland, W.: Branching time and abstraction in bisimulation semantics. In: Ritter, G.X. (ed.) Information Processing 89, Proc. of the IFIP World Computer Congress, pp. 613–618. North-Holland/IFIP, Amsterdam (1989)

    Google Scholar 

  12. Godefroid, P., Peled, D., Staskauskas, M.: Using partial order methods in the formal validation of industrial concurrent programs. In: Zeil, S.J. (ed.) Intl. Symp. on Software Testing and Analysis (ISSTA). Software Engineering Notes, vol. 21, pp. 261–269. ACM Press, New York (1996)

    Google Scholar 

  13. Godefroid, P., Pirottin, D.: Refining dependencies improves partial order verification methods. In: Courcoubetis, C. (ed.) Intl. Conf. on Computer-Aided Verification (CAV). LNCS, vol. 697, pp. 438–449. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  14. Godefroid, P., Wolper, P.: Using partial orders for the efficient verification of deadlock freedom and safety properties. In: Larsen, K.G., Skou, A. (eds.) Intl. Workshop on Computer-Aided Verification (CAV). LNCS, vol. 575, pp. 332–342. Springer, Heidelberg (1991)

    Chapter  Google Scholar 

  15. Godefroid, P., Wolper, P.: Using partial orders for the efficient verification of deadlock freedom and safety properties. Form. Methods Syst. Des. 2(2), 149–164 (1993)

    Article  Google Scholar 

  16. Holzmann, G., Godefroid, P., Pirottin, D.: Coverage preserving reduction strategies for reachability analysis. In: Linn, R.J. Jr., Uyar, M.Ü. (eds.) Intl. Symp. on Protocol Specification, Testing and Verification (PSTV). IFIP Transactions, vol. C-8, pp. 349–363. North-Holland, Amsterdam (1992)

    Chapter  Google Scholar 

  17. Holzmann, G., Peled, D.: An improvement in formal verification. In: Hogrefe, D., Leue, S. (eds.) Intl. Conf. on Formal Description Techniques (FORTE). IFIP Conference Proceedings, vol. 6, pp. 197–211. Chapman & Hall, London (1994)

    Google Scholar 

  18. Holzmann, G.J., Peled, D., Yannakakis, M.: On nested depth first search. In: Grégoire, J.C., Holzmann, G.J., Peled, D.A. (eds.) Workshop on the SPIN Verification System. DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, vol. 32, pp. 23–32. AMS/DIMACS, Providence (1996)

    Chapter  Google Scholar 

  19. Kahlon, V., Wang, C., Gupta, A.: Monotonic partial order reduction: an optimal symbolic partial order reduction technique. In: Bouajjani, A., Maler, O. (eds.) Intl. Conf. on Computer-Aided Verification (CAV). LNCS, vol. 5643, pp. 398–413. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  20. Katz, S., Peled, D.: An efficient verification method for parallel and distributed programs. In: de Bakker, J.W., de Roever, W.P., Rozenberg, G. (eds.) REX Workshop on Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency. LNCS, vol. 354, pp. 489–507. Springer, Heidelberg (1988)

    Chapter  Google Scholar 

  21. Katz, S., Peled, D.: Defining conditional independence using collapses. Theor. Comput. Sci. 101(2), 337–359 (1992)

    Article  MathSciNet  Google Scholar 

  22. Kokkarinen, I., Peled, D., Valmari, A.: Relaxed visibility enhances partial order reduction. In: Grumberg, O. (ed.) Intl. Conf. on Computer-Aided Verification (CAV). LNCS, vol. 1254, pp. 328–339. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  23. Kurshan, R., Levin, V., Minea, M., Peled, D., Yenigün, H.: Static partial order reduction. In: Steffen, B. (ed.) Intl. Conf. on Tools and Algorithms for the Construction and Analysis of Systems (TACAS). LNCS, vol. 1384, pp. 345–357. Springer, Heidelberg (1998)

    Google Scholar 

  24. Lamport, L.: What good is temporal logic. In: Mason, R. (ed.) Information Processing 83, Proc. of the World Computer Congress, pp. 657–668. North-Holland/IFIP, Amsterdam (1983)

    Google Scholar 

  25. Mazurkiewicz, A.: Trace theory. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) Petri Nets: Central Models and Their Properties, Advances in Petri Nets (APN). LNCS, vol. 255, pp. 279–324. Springer, Heidelberg (1986)

    Google Scholar 

  26. McMillan, K.L.: Using unfoldings to avoid the state explosion problem in the verification of asynchronous circuits. In: Gregor von Bochmann, D.K.P. (ed.) Intl. Workshop on Computer-Aided Verification (CAV). LNCS, vol. 663, pp. 164–177. Springer, Heidelberg (1992)

    Chapter  Google Scholar 

  27. Milner, R.: A Calculus of Communicating Systems. LNCS, vol. 92. Springer, Heidelberg (1980)

    MATH  Google Scholar 

  28. Ochmanski, E.: Languages and automata. In: Diekert, V., Rozenberg, G. (eds.) The Book of Traces, pp. 167–204. World Scientific, Singapore (1995)

    Chapter  Google Scholar 

  29. Peled, D.: All from one, one for all, on model-checking using representatives. In: Courcoubetis, C. (ed.) Intl. Conf. on Computer-Aided Verification (CAV). LNCS, vol. 697, pp. 409–423. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  30. Peled, D.: Combining partial order reductions with on-the-fly model-checking. Form. Methods Syst. Des. 8(1), 39–64 (1996)

    Article  Google Scholar 

  31. Peled, D., Wilke, T.: Stutter-invariant temporal properties are expressible without the nexttime operator. Inf. Process. Lett. 63(5), 243–246 (1997)

    Article  Google Scholar 

  32. Peled, D., Wilke, T., Wolper, P.: An algorithmic approach for checking closure properties of \(\omega\)-regular languages. In: Intl. Conf. on Concurrency Theory (CONCUR). LNCS, vol. 1119, pp. 596–610. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  33. Valmari, A.: Stubborn sets for reduced state space generation. In: Rozenberg, G. (ed.) Intl. Conf. on Applications and Theory of Petri Nets (APN). LNCS, vol. 483, pp. 491–515. Springer, Heidelberg (1989)

    Google Scholar 

  34. Valmari, A.: On-the-fly verification with stubborn sets. In: Courcoubetis, C. (ed.) Intl. Conf. on Computer-Aided Verification (CAV). LNCS, vol. 697, pp. 397–408. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  35. Valmari, A.: Stubborn set methods for process algebras. In: Peled, D.A., Pratt, V.R., Holzmann, G.J. (eds.) DIMACS Workshop on Partial Order Methods in Verification (POMIV). DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 29, pp. 213–231. AMS, Providence (1996)

    Chapter  Google Scholar 

  36. Vardi, M., Wolper, P.: An automata-theoretic approach to automatic program verification. In: Symp. on Logic in Computer Science (LICS), pp. 322–331. IEEE, Piscataway (1986)

    Google Scholar 

  37. Winskel, G.: An introduction to event structures. In: de Bakker, J.W., de Roever, W.P., Rozenberg, G. (eds.) REX Workshop on Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency. LNCS, vol. 354, pp. 364–397. Springer, Heidelberg (1988)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Doron Peled .

Editor information

Editors and Affiliations

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

Peled, D. (2018). Partial-Order Reduction. 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_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-10575-8_6

  • 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