Proving Linearizability Using Partial Orders

  • Artem KhyzhaEmail author
  • Mike Dodds
  • Alexey Gotsman
  • Matthew Parkinson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10201)


Linearizability is the commonly accepted notion of correctness for concurrent data structures. It requires that any execution of the data structure is justified by a linearization—a linear order on operations satisfying the data structure’s sequential specification. Proving linearizability is often challenging because an operation’s position in the linearization order may depend on future operations. This makes it very difficult to incrementally construct the linearization in a proof.

We propose a new proof method that can handle data structures with such future-dependent linearizations. Our key idea is to incrementally construct not a single linear order of operations, but a partial order that describes multiple linearizations satisfying the sequential specification. This allows decisions about the ordering of operations to be delayed, mirroring the behaviour of data structure implementations. We formalise our method as a program logic based on rely-guarantee reasoning, and demonstrate its effectiveness by verifying several challenging data structures: the Herlihy-Wing queue, the TS queue and the Optimistic set.


Program Logic Atomic Step Forward Simulation Abstract History Proof Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Dinsdale-Young, T., Dodds, M., Gardner, P., Parkinson, M.J., Vafeiadis, V.: Concurrent abstract predicates. In: D’Hondt, T. (ed.) ECOOP 2010. LNCS, vol. 6183, pp. 504–528. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-14107-2_24 CrossRefGoogle Scholar
  2. 2.
    Dodds, M., Haas, A., Kirsch, C.M.: A scalable, correct time-stamped stack. In: POPL (2015)Google Scholar
  3. 3.
    Dongol, B., Derrick, J.: Verifying linearizability: a comparative survey. arXiv CoRR, 1410.6268 (2014)Google Scholar
  4. 4.
    Filipovic, I., O’Hearn, P.W., Rinetzky, N., Yang, H.: Abstraction for concurrent objects. Theor. Comput. Sci. 411(51–52), 4379–4398 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Fishburn, P.C.: Intransitive indifference with unequal indifference intervals. J. Math. Psychol. 7, 144–149 (1970)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Gotsman, A., Yang, H.: Linearizability with ownership transfer. In: Koutny, M., Ulidowski, I. (eds.) CONCUR 2012. LNCS, vol. 7454, pp. 256–271. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-32940-1_19 CrossRefGoogle Scholar
  7. 7.
    Haas, A.: Fast concurrent data structures through timestamping. Ph.D. thesis, University of Salzburg (2015)Google Scholar
  8. 8.
    Heller, S., Herlihy, M., Luchangco, V., Moir, M., Scherer, W.N., Shavit, N.: A lazy concurrent list-based set algorithm. In: Anderson, J.H., Prencipe, G., Wattenhofer, R. (eds.) OPODIS 2005. LNCS, vol. 3974, pp. 3–16. Springer, Heidelberg (2006). doi: 10.1007/11795490_3 CrossRefGoogle Scholar
  9. 9.
    Hemed, N., Rinetzky, N., Vafeiadis, V.: Modular verification of concurrency-aware linearizability. In: Moses, Y. (ed.) DISC 2015. LNCS, vol. 9363, pp. 371–387. Springer, Heidelberg (2015). doi: 10.1007/978-3-662-48653-5_25 CrossRefGoogle Scholar
  10. 10.
    Henzinger, T.A., Sezgin, A., Vafeiadis, V.: Aspect-oriented linearizability proofs. In: D’Argenio, P.R., Melgratti, H. (eds.) CONCUR 2013. LNCS, vol. 8052, pp. 242–256. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-40184-8_18 CrossRefGoogle Scholar
  11. 11.
    Herlihy, M., Wing, J.M.: Linearizability: a correctness condition for concurrent objects. In: ACM TOPLAS (1990)Google Scholar
  12. 12.
    Hoffman, M., Shalev, O., Shavit, N.: The baskets queue. In: Tovar, E., Tsigas, P., Fouchal, H. (eds.) OPODIS 2007. LNCS, vol. 4878, pp. 401–414. Springer, Heidelberg (2007). doi: 10.1007/978-3-540-77096-1_29 CrossRefGoogle Scholar
  13. 13.
    Jones, C.B.: Specification and design of (parallel) programs. In: IFIP Congress (1983)Google Scholar
  14. 14.
    Khyzha, A., Dodds, M., Gotsman, A., Parkinson, M.: Proving linearizability using partial orders (extended version). arXiv CoRR, 1701.05463 (2017)Google Scholar
  15. 15.
    Liang, H., Feng, X.: Modular verification of linearizability with non-fixed linearization points. In: PLDI (2013)Google Scholar
  16. 16.
    Morrison, A., Afek, Y.: Fast concurrent queues for x86 processors. In: PPoPP (2013)Google Scholar
  17. 17.
    O’Hearn, P.W., Rinetzky, N., Vechev, M.T., Yahav, E., Yorsh, G.: Verifying linearizability with hindsight. In: PODC (2010)Google Scholar
  18. 18.
    Owicki, S.S., Gries, D.: An axiomatic proof technique for parallel programs I. Acta Informatica 6, 319–340 (1976)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Schellhorn, G., Derrick, J., Wehrheim, H.: A sound and complete proof technique for linearizability of concurrent data structures. ACM TOCL 15(4), 31 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Turon, A., Dreyer, D., Birkedal, L.: Unifying refinement and hoare-style reasoning in a logic for higher-order concurrency. In: ICFP (2013)Google Scholar
  21. 21.
    Turon, A.J., Thamsborg, J., Ahmed, A., Birkedal, L., Dreyer, D.: Logical relations for fine-grained concurrency. In: POPL (2013)Google Scholar
  22. 22.
    Vafeiadis, V.: Modular fine-grained concurrency verification. Ph.D. thesis, University of Cambridge, UK (2008). Technical report UCAM-CL-TR-726Google Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Artem Khyzha
    • 1
    Email author
  • Mike Dodds
    • 2
  • Alexey Gotsman
    • 1
  • Matthew Parkinson
    • 3
  1. 1.IMDEA Software InstituteMadridSpain
  2. 2.University of YorkYorkUK
  3. 3.Microsoft ResearchCambridgeUK

Personalised recommendations