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Verifying a quantitative relaxation of linearizability via refinement

  • Kiran Adhikari
  • James Street
  • Chao WangEmail author
  • Yang Liu
  • Shaojie Zhang
SPIN 2013

Abstract

The recent years have seen increasingly widespread use of highly concurrent data structures in both multi-core and distributed computing environments, thereby escalating the priority for verifying their correctness. Quasi linearizability is a quantitative variation of the standard linearizability correctness condition to allow more implementation freedom for performance optimization. However, ensuring that the implementation satisfies the quantitative aspect of this new correctness condition is often an arduous task. In this paper, we propose the first automated method for formally verifying quasi linearizability of the implementation model of a concurrent data structure with respect to its sequential specification. The method is based on checking a relaxed version of the refinement relation between the implementation model and the specification model through explicit state model checking. Our method can directly handle concurrent systems where each thread or process makes infinitely many method calls. Furthermore, unlike many existing verification methods, it does not require the user to supply annotations of the linearization points. We have implemented the new method in the PAT verification framework. Our experimental evaluation shows that the method is effective in verifying the new quasi linearizability requirement and detecting violations.

Keywords

Linearizability Model checking Concurrent data structure Refinement Quantitative relaxation 

Notes

Acknowledgments

This research was supported by the U.S. National Science Foundation under Grant Number CCF-1149454. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation.

References

  1. 1.
    Afek, Y., Korland, G., Yanovsky, E.: Quasi-linearizability: relaxed consistency for improved concurrency. In: International Conference on Principles of Distributed Systems, pp. 395–410 (2010)Google Scholar
  2. 2.
    Aspnes, J., Herlihy, M., Shavit, N.: Counting networks. J. ACM. 41(5), 1020–1048 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Attiya, H., Welch, J.: Distributed computing: fundamentals, simulations, and advanced topics, 2nd edn. John Wiley and Sons Inc., Publication, New Jersey (2004)CrossRefzbMATHGoogle Scholar
  4. 4.
    Burckhardt, S., Dern, C., Musuvathi, M., Tan, R.: Line-up: a complete and automatic linearizability checker. In: ACM SIGPLAN Conference on Programming Language Design and Implementation, pp. 330–340 (2010)Google Scholar
  5. 5.
    Cerný, P., Radhakrishna, A., Zufferey, D., Chaudhuri, S., Alur, R.: Model checking of linearizability of concurrent list implementations. In: International Conference on Computer Aided Verification, pp. 465–479 (2010)Google Scholar
  6. 6.
    Farzan, A., Madhusudan, P.: Monitoring atomicity in concurrent programs. In: International Conference on Computer Aided Verification, pp. 52–65 (2008)Google Scholar
  7. 7.
    Flanagan, C., Qadeer, S.: A type and effect system for atomicity. In: ACM SIGPLAN Conference on Programming Language Design and Implementation, pp. 338–349 (2003)Google Scholar
  8. 8.
    Ganai, M.K., Arora, N., Wang, C., Gupta, A., Balakrishnan, G.: BEST: A symbolic testing tool for predicting multi-threaded program failures. In: IEEE/ACM International Conference on Automated Software Engineering, (2011)Google Scholar
  9. 9.
    Haas, A., Lippautz, M., Henzinger, T.A., Payer, H., Sokolova, A., Kirsch, C.M., Sezgin, A.: Distributed queues in shared memory: multicore performance and scalability through quantitative relaxation. In: Conference Computing Frontiers, p. 17 (2013)Google Scholar
  10. 10.
    Henzinger, T.A., Sezgin, A., Kirsch, C.M., Payer, H., Sokolova, A.:. Quantitative relaxation of concurrent data structures. In: ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages, pp. 317–328 (2013)Google Scholar
  11. 11.
    Herlihy, M., Shavit, N.: The art of multiprocessor programming. Morgan Kaufmann, USA (2008)Google Scholar
  12. 12.
    Herlihy, M., Wing, J.M.: Linearizability: a correctness condition for concurrent objects. ACM. Trans. Program. Lang. Syst. 12(3), 463–492 (1990)CrossRefGoogle Scholar
  13. 13.
    Hoare, C.A.R.: Communicating sequential processes. Prentice Hall, Englewood Cliffs (1985)zbMATHGoogle Scholar
  14. 14.
    Kirsch, C.M. Payer, H.: Incorrect systems: it’s not the problem, it’s the solution. In: Proceedings of the Design Automation Conference, pp. 913–917 (2012)Google Scholar
  15. 15.
    Kirsch, C.M., Payer, H., Röck, H., Sokolova, A.: Performance, scalability, and semantics of concurrent fifo queues. In: ICA3PP, pp. 273–287 (2012)Google Scholar
  16. 16.
    Lamport, L.: How to make a multiprocessor computer that correctly executes multiprocess programs. IEEE. Trans. Comput. 28(9), 690–691 (1979)CrossRefzbMATHGoogle Scholar
  17. 17.
    Liu, Y., Chen, W., Liu, Y., Zhang, S., Sun, J., Dong, J.S.: Verifying linearizability via optimized refinement checking. IEEE. Trans. Softw. Eng. (2013)Google Scholar
  18. 18.
    Liu, Y., Chen, W., Liu, Y.A., Sun, J.: Model checking linearizability via refinement. In: International Symposium on Formal Methods, pp. 321–337 (2009)Google Scholar
  19. 19.
    Lynch, N.: Distributed algorithms. Morgan Kaufmann, USA (1997)Google Scholar
  20. 20.
    Michael, M.M., Vechev, M.T., Saraswat, V.A.: Idempotent work stealing. In: ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming, Raleigh, pp. 45–54 (2009)Google Scholar
  21. 21.
    Payer, H., Röck, H., Kirsch, C.M., Sokolova, A.: Scalability versus semantics of concurrent fifo queues. In: ACM Symposium on Principles of Distributed Computing, pp. 331–332 (2011)Google Scholar
  22. 22.
    Said, M., Wang, C., Yang, Z., Sakallah, K.: Generating data race witnesses by an SMT-based analysis. In: NASA Formal Methods, pp. 313–327 (2011)Google Scholar
  23. 23.
    Sinha, A., Malik, S., Wang, C., Gupta, A.: Predicting serializability violations: SMT-based search vs. DPOR-based search. In: Haifa Verification Conference, pp. 95–114 (2011)Google Scholar
  24. 24.
    Sinha, A., Malik, S., Wang, C., Gupta, A.: Predictive analysis for detecting serializability violations through trace segmentation. In: Formal Methods and Models for Codesign, pp. 99–108 (2011)Google Scholar
  25. 25.
    Sinha, N., Wang, C.: Staged concurrent program analysis. In: ACM SIGSOFT Symposium on Foundations of Software Engineering, pp. 47–56 (2010)Google Scholar
  26. 26.
    Sun, J., Liu, Y., Dong, J.S., Chen, C.: Integrating specification and programs for system modeling and verification. In: International Symposium on Theoretical Aspects of Software Engineering, pp. 127–135 (2009)Google Scholar
  27. 27.
    Sun, J., Liu, Y., Dong, J.S., Pang, J.: PAT: Towards Flexible Verification under Fairness. In: International Conference on Computer Aided Verification, pp. 709–714 (2009)Google Scholar
  28. 28.
    Treiber, R.K.: Systems programming: coping with parallelism. Technical Report RJ 5118, IBM Almaden Research Center (1986)Google Scholar
  29. 29.
    Vafeiadis, V.: Shape-value abstraction for verifying linearizability. In: International Conference on Verification, Model Checking, and Abstract Interpretation, pp. 335–348 (2009)Google Scholar
  30. 30.
    Vafeiadis, V., Herlihy, M., Hoare, T., Shapiro, M.: Proving correctness of highly-concurrent linearisable objects. In: ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming, pp. 129–136 (2006)Google Scholar
  31. 31.
    Vechev, M.T., Yahav, E., Yorsh, G.: Experience with model checking linearizability. In: International SPIN Workshop on Model Checking Software, pp. 261–278 (2009)Google Scholar
  32. 32.
    Vogels, W.: Eventually consistent. Commun. ACM. 52(1), 40–44 (2009)CrossRefGoogle Scholar
  33. 33.
    Wang, C., Ganai, M.: Predicting concurrency failures in generalized traces of x86 executables. In: International Conference on Runtime Verification (2011)Google Scholar
  34. 34.
    Wang, C., Hoang, K.: Precisely deciding control state reachability in concurrent traces with limited observability. In: International Conference on Verification, Model Checking, and Abstract Interpretation, pp. 376–394 (2014)Google Scholar
  35. 35.
    Wang, C., Kundu, S., Ganai, M., Gupta, A.: Symbolic predictive analysis for concurrent programs. In: International Symposium on Formal Methods, pp. 256–272 (2009)Google Scholar
  36. 36.
    Wang, C., Limaye, R., Ganai, M., Gupta, A.: Trace-based symbolic analysis for atomicity violations. In: International Conference on Tools and Algorithms for Construction and Analysis of Systems, pp. 328–342 (2010)Google Scholar
  37. 37.
    Wang, C., Yang, Y., Gupta, A., Gopalakrishnan, G.: Dynamic model checking with property driven pruning to detect race conditions. In: International Symposium on Automated Technology for Verification and Analysis, pp. 126–140 (2008)Google Scholar
  38. 38.
    Wang, L., Stoller, S.D.: Runtime analysis of atomicity for multithreaded programs. IEEE. Trans. Softw. Eng. 32(2), 93–110 (2006)CrossRefGoogle Scholar
  39. 39.
    Zhang, L., Chattopadhyay, A., Wang, C.: Round-Up: Runtime checking quasi linearizability of concurrent data structures. In: IEEE/ACM International Conference on Automated Software Engineering, pp. 4–14 (2013)Google Scholar
  40. 40.
    Zhang, L., Wang, C.: Runtime prevention of concurrency related type-state violations in multithreaded applications. In: International Symposium on Software Testing and Analysis, pp. 1–12 (2014)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Kiran Adhikari
    • 1
  • James Street
    • 1
  • Chao Wang
    • 1
    Email author
  • Yang Liu
    • 2
  • Shaojie Zhang
    • 3
  1. 1.Virginia TechBlacksburgUSA
  2. 2.Nanyang Technological UniversitySingaporeSingapore
  3. 3.Singapore University of Technology and DesignSingaporeSingapore

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