Skip to main content
SpringerLink
Log in

Quasi-Linearizability is Undecidable

  • Conference paper
  • First Online:
Programming Languages and Systems (APLAS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9458))

Included in the following conference series:

Abstract

Quasi-linearizability is a quantitative relaxation of linearizability. It preserves the intuition of the standard notion of linearizability and permits more flexibility. The decidability of quasi-linearizability has been remaining open in general for a bounded number of processes. In this paper we show that the problem of whether a library is quasi-linearizable with respect to a regular sequential specification is undecidable for a bounded number of processes. This is proved by reduction from the k-Z decision problem of a k-counter machine, a known undecidable problem. The key idea of the proof is to establish a correspondence between the quasi-sequential specification of quasi-linearizability and the set of all unadmitted runs of the k-counter machines.

This work is partially supported by the National Natural Science Foundation of China under Grants No.60721061, No.60833001, No.61272135, No.61700073, No.61100069, No.61472405, and No.61161130530.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Except the \(\textit{cas}\) operation, other operations, such as filter lock [10] can also be used herein to ensure mutual exclusion.

References

  1. Adhikari, K., Street, J., Wang, C., Liu, Y., Zhang, S.J.: Verifying a quantitative relaxation of linearizability via refinement. In: Bartocci, E., Ramakrishnan, C.R. (eds.) SPIN 2013. LNCS, vol. 7976, pp. 24–42. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  2. Afek, Y., Korland, G., Yanovsky, E.: Quasi-linearizability: relaxed consistency for improved concurrency. In: Lu, C., Masuzawa, T., Mosbah, M. (eds.) OPODIS 2010. LNCS, vol. 6490, pp. 395–410. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  3. Alur, R., McMillan, K., Peled, D.: Model-checking of correctness conditions for concurrent objects. In: LICS 1996, pp. 219–228. IEEE Computer Society (1996)

    Google Scholar 

  4. Aspnes, J., Herlihy, M., Shavit, N.: Counting networks. J. ACM 41(5), 1020–1048 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bouajjani, A., Emmi, M., Enea, C., Hamza, J.: Verifying concurrent programs against sequential specifications. In: Felleisen, M., Gardner, P. (eds.) ESOP 2013. LNCS, vol. 7792, pp. 290–309. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  6. Bouajjani, A., Emmi, M., Enea, C., Hamza, J.: Tractable refinement checking for concurrent objects. In: Rajamani, S.K., Walker, D. (eds.) POPL 2015, pp. 651–662. ACM (2015)

    Google Scholar 

  7. Burckhardt, S., Gotsman, A., Musuvathi, M., Yang, H.: Concurrent library correctness on the TSO memory model. In: Seidl, H. (ed.) Programming Languages and Systems. LNCS, vol. 7211, pp. 87–107. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  8. Černý, P., Radhakrishna, A., Zufferey, D., Chaudhuri, S., Alur, R.: Model checking of linearizability of concurrent list implementations. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 465–479. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  9. Henzinger, T.A., Kirsch, C.M., Payer, H., Sezgin, A., Sokolova, A.: Quantitative relaxation of concurrent data structures. In: Giacobazzi, R., Cousot, R. (eds.) POPL 2013, pp. 317–328. ACM (2013)

    Google Scholar 

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

    Google Scholar 

  11. Herlihy, M.P., Wing, J.M.: Linearizability: a correctness condition for concurrent objects. ACM Trans. Program. Lang. Syst. 12(3), 463–492 (1990)

    Article  Google Scholar 

  12. Lamport, L.: How to make a multiprocessor computer that correctly executes multiprocess program. IEEE Trans. Comput. 28(9), 690–691 (1979)

    Article  MATH  Google Scholar 

  13. Zhang, L., Chattopadhyay, A., Wang, C.: Round-up: Runtime checking quasi linearizability of concurrent data structures. In: Denney, E., Bultan, T., Zeller, A. (eds.) ASE 2013, pp. 4–14. IEEE (2013)

    Google Scholar 

Download references

Acknowledgments

The authors of this paper would like to thank anonymous reviewers for pointing out the connection between dependence relations in [3] and quasi-linearization factors in [2].

Author information

Authors and Affiliations

  1. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China

    Chao Wang, Yi Lv, Gaoang Liu & Peng Wu

  2. University of Chinese Academy of Sciences, Beijing, China

    Chao Wang & Gaoang Liu

Authors
  1. Chao Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yi Lv
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gaoang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Peng Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chao Wang .

Editor information

Editors and Affiliations

  1. Univ. of Science and Technology of China, Hefei, Anhui, China

    Xinyu Feng

  2. Pohang Univ. of Science and Technology, Nam-Gu, Pohang, Korea (Republic of)

    Sungwoo Park

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Wang, C., Lv, Y., Liu, G., Wu, P. (2015). Quasi-Linearizability is Undecidable. In: Feng, X., Park, S. (eds) Programming Languages and Systems. APLAS 2015. Lecture Notes in Computer Science(), vol 9458. Springer, Cham. https://doi.org/10.1007/978-3-319-26529-2_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-26529-2_20

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26528-5

  • Online ISBN: 978-3-319-26529-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation