Skip to main content
Springer Nature Link
Log in

Towards Efficient Runtime Verified Linearizable Algorithms

  • Conference paper
  • First Online:
Runtime Verification (RV 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 15191))

Included in the following conference series:

  • 107 Accesses

Abstract

An asynchronous, fault-tolerant, sound and complete algorithm for runtime verification of linearizability of concurrent algorithms was proposed in [7]. This solution relies on the snapshot abstraction in distributed computing. The fastest known snapshot algorithms use complex constructions, hard to implement, and the simplest ones provide large step complexity bounds or only weak termination guarantees. Thus, the snapshot-based verification algorithm is not completely satisfactory. In this paper, we propose an alternative solution, based on the collect abstraction, which can be optimally implemented in a simple manner. As a final result, we offer a simple and generic methodology that takes any presumably linearizable algorithm and produces a lightweight runtime verified linearizable version of it.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    We can eliminate this assumption; we assume it to simplify the algorithm.

  2. 2.

    \(\mathcal {A^{*}}\) can invoke any high-level operation of \(\mathcal {A}\), denoted as Apply(\(op_i\)) [7].

  3. 3.

    The response event happens immediately, e.g., the tight execution in Fig. 1.

  4. 4.

    Theorem 1 appears to be a straightforward way to verify \(\mathcal {A^{+}}\), but due to asynchrony we do not obtain an \(X_E\) thought \(\mathcal {V^{+}}\); however, we can transform any \(X(\tau _i)\) into a well-formed execution \(X(\tau _i')\) which is also an sketch of an execution \(\mathcal {A^{+}}\) as \(X_E\).

  5. 5.

    We focus on the case that each entry stores an evergrowing set, but the definition can be generalized.

References

  1. Afek, Y., Attiya, H., Dolev, D., Gafni, E., Merritt, M., Shavit, N.: Atomic snapshots of shared memory. J. ACM 40(4), 873–890 (1993). https://doi.org/10.1145/153724.153741

    Article  Google Scholar 

  2. Bartocci, E., Falcone, Y. (eds.): Lectures on Runtime Verification - Introductory and Advanced Topics. Lecture Notes in Computer Science, vol. 10457. Springer, Cham (2018)https://doi.org/10.1007/978-3-319-75632-5

  3. Bashari, B., Woelfel, P.: An efficient adaptive partial snapshot implementation. In: Miller, A., Censor-Hillel, K., Korhonen, J.H. (eds.) PODC 2021: ACM Symposium on Principles of Distributed Computing, Virtual Event, Italy, 26–30 July 2021, pp. 545–555. ACM (2021). https://doi.org/10.1145/3465084.3467939

  4. Berkovich, S., Bonakdarpour, B., Fischmeister, S.: Runtime verification with minimal intrusion through parallelism. Formal Methods Syst. Des. 46(3), 317–348 (2015). https://doi.org/10.1007/s10703-015-0226-3

    Article  Google Scholar 

  5. Bonakdarpour, B., Fraigniaud, P., Rajsbaum, S., Rosenblueth, D.A., Travers, C.: Decentralized asynchronous crash-resilient runtime verification. J. ACM 69(5), 34:1–34:31 (2022). https://doi.org/10.1145/3550483

  6. Bonakdarpour, B., Fraigniaud, P., Rajsbaum, S., Travers, C.: Challenges in fault-tolerant distributed runtime verification. In: Margaria, T., Steffen, B. (eds.) ISoLA 2016, Part II. LNCS, vol. 9953, pp. 363–370. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-47169-3_27

    Chapter  Google Scholar 

  7. Castañeda, A., Rodríguez, G.V.: Asynchronous wait-free runtime verification and enforcement of linearizability. In: Oshman, R., Nolin, A., Halldórsson, M.M., Balliu, A. (eds.) Proceedings of the 2023 ACM Symposium on Principles of Distributed Computing, PODC 2023, Orlando, FL, USA, 19–23 June 2023, pp. 90–101. ACM (2023). https://doi.org/10.1145/3583668.3594563

  8. Decker, N., Gottschling, P., Hochberger, C., Leucker, M., Scheffel, T., Schmitz, M., Weiss, A.: Rapidly adjustable non-intrusive online monitoring for multi-core systems. In: Cavalheiro, S., Fiadeiro, J. (eds.) SBMF 2017. LNCS, vol. 10623, pp. 179–196. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70848-5_12

    Chapter  Google Scholar 

  9. El-Hokayem, A., Falcone, Y.: Can we monitor all multithreaded programs? In: Colombo, C., Leucker, M. (eds.) RV 2018. LNCS, vol. 11237, pp. 64–89. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03769-7_6

    Chapter  Google Scholar 

  10. Elmas, T., Tasiran, S.: Vyrdmc: Driving runtime refinement checking with model checkers. In: Barringer, H., Finkbeiner, B., Gurevich, Y., Sipma, H. (eds.) Proceedings of the Fifth Workshop on Runtime Verification, RV@CAV 2005, Edinburgh, UK, 12 July 2005. Electronic Notes in Theoretical Computer Science, vol. 144, pp. 41–56. Elsevier (2005). https://doi.org/10.1016/j.entcs.2006.02.003

  11. Elmas, T., Tasiran, S., Qadeer, S.: VYRD: verifying concurrent programs by runtime refinement-violation detection. In: Sarkar, V., Hall, M.W. (eds.) Proceedings of the ACM SIGPLAN 2005 Conference on Programming Language Design and Implementation, Chicago, IL, USA, 12–15 June 2005, pp. 27–37. ACM (2005). https://doi.org/10.1145/1065010.1065015

  12. Falcone, Y.: On decentralized monitoring. In: Nouri, A., Wu, W., Barkaoui, K., Li, Z.W. (eds.) VECoS 2021. LNCS, vol. 13187, pp. 1–16. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-98850-0_1

    Chapter  Google Scholar 

  13. Falcone, Y., Havelund, K., Reger, G.: A tutorial on runtime verification. In: Broy, M., Peled, D.A., Kalus, G. (eds.) Engineering Dependable Software Systems, NATO Science for Peace and Security Series, D: Information and Communication Security, vol. 34, pp. 141–175. IOS Press (2013). https://doi.org/10.3233/978-1-61499-207-3-141

  14. Fraigniaud, P., Rajsbaum, S., Travers, C.: Locality and checkability in wait-free computing. Distrib. Comput. 26(4), 223–242 (2013). https://doi.org/10.1007/s00446-013-0188-x

    Article  Google Scholar 

  15. Fraigniaud, P., Rajsbaum, S., Travers, C.: A lower bound on the number of opinions needed for fault-tolerant decentralized run-time monitoring. J. Appl. Comput. Topol. 4(1), 141–179 (2020). https://doi.org/10.1007/s41468-019-00047-6

    Article  MathSciNet  Google Scholar 

  16. Francalanza, A., Pérez, J.A., Sánchez, C.: Runtime verification for decentralised and distributed systems. In: Bartocci, E., Falcone, Y. (eds.) Lectures on Runtime Verification. LNCS, vol. 10457, pp. 176–210. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-75632-5_6

    Chapter  Google Scholar 

  17. Havelund, K., Goldberg, A.: Verify your runs. In: Meyer, B., Woodcock, J. (eds.) VSTTE 2005. LNCS, vol. 4171, pp. 374–383. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-69149-5_40

    Chapter  Google Scholar 

  18. Herlihy, M.: Wait-free synchronization. ACM Trans. Program. Lang. Syst. 13(1), 124–149 (1991). https://doi.org/10.1145/114005.102808

    Article  Google Scholar 

  19. Herlihy, M., Kozlov, D.N., Rajsbaum, S.: Distributed Computing Through Combinatorial Topology. Morgan Kaufmann (2013). https://store.elsevier.com/product.jsp?isbn=9780124045781

  20. Herlihy, M., Shavit, N.: The Art of Multiprocessor Programming. Morgan Kaufmann (2008)

    Google Scholar 

  21. Herlihy, M., Wing, J.M.: Linearizability: a correctness condition for concurrent objects. ACM Trans. Program. Lang. Syst. 12(3), 463–492 (1990). https://doi.org/10.1145/78969.78972

    Article  Google Scholar 

  22. Inoue, M., Masuzawa, T., Chen, W., Tokura, N.: Linear-time snapshot using multi-writer multi-reader registers. In: Tel, G., Vitányi, P. (eds.) WDAG 1994. LNCS, vol. 857, pp. 130–140. Springer, Heidelberg (1994). https://doi.org/10.1007/BFb0020429

    Chapter  Google Scholar 

  23. Kuznetsov, P., Guerraoui, R.: Algorithms for Concurrent Systems. EPFL Press (2018)

    Google Scholar 

  24. Lamport, L.: How to make a multiprocessor computer that correctly executes multiprocess programs. IEEE Trans. Comput. 28(9), 690–691 (1979). https://doi.org/10.1109/TC.1979.1675439

    Article  Google Scholar 

  25. Leucker, M., Schallhart, C.: A brief account of runtime verification. J. Log. Algebraic Methods Program. 78, 293–303 (2009). https://doi.org/10.1016/j.jlap.2008.08.004

    Article  Google Scholar 

  26. Lourenço, J.M., Fiedor, J., Křena, B., Vojnar, T.: Discovering concurrency errors. In: Bartocci, E., Falcone, Y. (eds.) Lectures on Runtime Verification. LNCS, vol. 10457, pp. 34–60. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-75632-5_2

    Chapter  Google Scholar 

  27. Lynch, N.A., Vaandrager, F.W.: Forward and backward simulations: I. Untimed systems. Inf. Comput. 121(2), 214–233 (1995). https://doi.org/10.1006/inco.1995.1134

    Article  MathSciNet  Google Scholar 

  28. Moir, M., Shavit, N.: Concurrent data structures. In: Mehta, D.P., Sahni, S. (eds.) Handbook of Data Structures and Applications. Chapman and Hall/CRC (2004). https://doi.org/10.1201/9781420035179.ch47

  29. Pnueli, A., Zaks, A.: PSL model checking and run-time verification via testers. In: Misra, J., Nipkow, T., Sekerinski, E. (eds.) FM 2006. LNCS, vol. 4085, pp. 573–586. Springer, Heidelberg (2006). https://doi.org/10.1007/11813040_38

    Chapter  Google Scholar 

  30. Raynal, M.: Concurrent Programming - Algorithms, Principles, and Foundations. Springer, Cham (2012). https://doi.org/10.1007/978-3-642-32027-9

  31. Sánchez, C., et al.: A survey of challenges for runtime verification from advanced application domains (beyond software). Formal Methods Syst. Des. 54(3), 279–335 (2019). https://doi.org/10.1007/s10703-019-00337-w

    Article  Google Scholar 

  32. Soueidi, C., El-Hokayem, A., Falcone, Y.: Opportunistic monitoring of multithreaded programs. In: Lambers, L., Uchitel, S. (eds.) FASE 2023. LNCS, vol. 13991, pp. 173–194. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-30826-0_10

    Chapter  Google Scholar 

  33. Taleb, R., Hallé, S., Khoury, R.: Uncertainty in runtime verification: A survey. Comput. Sci. Rev. 50, 100594 (2023). https://doi.org/10.1016/J.COSREV.2023.100594

    Article  MathSciNet  Google Scholar 

  34. Wei, Y., Ben-David, N., Blelloch, G.E., Fatourou, P., Ruppert, E., Sun, Y.: Constant-time snapshots with applications to concurrent data structures. In: Lee, J., Petrank, E. (eds.) PPoPP 2021: 26th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming, Virtual Event, Republic of Korea, 27 February–3 March 2021, pp. 31–46. ACM (2021). https://doi.org/10.1145/3437801.3441602

Download references

Acknowledgments

Gilde Valeria Rodríguez is the recipient of a PhD fellowship of CONAHCYT. Armando Castañeda is supported by the research project DGAPA-PAPIIT IN108723.

Author information

Authors and Affiliations

  1. Posgrado en Ciencia e Ingeniería de la Computación, Universidad Nacional Autónoma de México, Mexico City, Mexico

    Gilde Valeria Rodríguez

  2. Instituto de Matemáticas, Universidad Nacional Autónoma de México, Mexico City, Mexico

    Armando Castañeda

Authors
  1. Gilde Valeria Rodríguez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Armando Castañeda
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gilde Valeria Rodríguez .

Editor information

Editors and Affiliations

  1. RWTH Aachen University, Aachen, Nordrhein-Westfalen, Germany

    Erika Ábrahám

  2. Oregon State University, Corvallis, OR, USA

    Houssam Abbas

Rights and permissions

Reprints and permissions

Copyright information

© 2025 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Rodríguez, G.V., Castañeda, A. (2025). Towards Efficient Runtime Verified Linearizable Algorithms. In: Ábrahám, E., Abbas, H. (eds) Runtime Verification. RV 2024. Lecture Notes in Computer Science, vol 15191. Springer, Cham. https://doi.org/10.1007/978-3-031-74234-7_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-74234-7_17

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-74233-0

  • Online ISBN: 978-3-031-74234-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics