[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Nonatomic dual bakery algorithm with bounded tokens

  • Original Article
  • Published:
Acta Informatica Aims and scope Submit manuscript

Abstract

A simple mutual exclusion algorithm is presented that only uses nonatomic shared variables of bounded size, and that satisfies bounded overtaking. When the shared variables behave atomically, it has the first-come-first-served property (FCFS). Nonatomic access makes information vulnerable. The effects of this can be mitigated by minimizing the information and by spreading it over more variables. The design approach adopted here begins with such mitigating efforts. These resulted in an algorithm with a proof of correctness, first for atomic variables. This proof is then used as a blueprint for the simultaneous development of the algorithm for nonatomic variables and its proof. Mutual exclusion is proved by means of invariants. Bounded overtaking and liveness under weak fairness are proved with invariants and variant functions. Liveness under weak fairness is formalized and proved in a set-theoretic version of temporal logic. All these assertions are verified with the proof assistant PVS. We heavily rely on the possibility offered by a proof assistant like PVS to reuse proofs developed for one context in a different context.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abadi M., Lamport L.: The existence of refinement mappings. Theor. Comput. Sci. 82, 253–284 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  2. Abraham, U.: Bakery algorithms. In: Proceedings of the Concurrency, Specification, and Programming Workshop, pp. 7–40 (1993)

  3. Anderson J.H.: A fine-grained solution to the mutual exclusion problem. Acta Inf. 30(3), 249–265 (1993)

    Article  MATH  Google Scholar 

  4. Anderson J.H., Kim Y.J., Herman T.: Shared-memory mutual exclusion: major research trends since 1986. Distrib. Comput. 16, 75–110 (2003)

    Article  Google Scholar 

  5. Aravind A.: An arbitration algorithm for multiport memory systems. IEICE Electron. Express 2, 488–494 (2005)

    Article  Google Scholar 

  6. Aravind A.A., Hesselink W.H.: A queue based mutual exclusion algorithm. Acta Inf. 46, 73–86 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  7. Dijkstra E.W.: Solution of a problem in concurrent programming control. Commun. ACM 8, 569 (1965)

    Article  Google Scholar 

  8. Dijkstra E.W.: Co-operating sequential processes. In: Genuys, F. (ed.) Programming Languages, London, etc, pp. 43–112. NATO Advanced Study Institute, Academic Press, London (1968)

    Google Scholar 

  9. Haldar, S., Subramanian, P.S.: Space-optimum conflict-free construction of 1-writer 1-reader multivalued atomic variable. In: Proceedings of the 8th International Workshop on Distributed Algorithms, volume 857 of LNCS, pp. 116–129. Springer, Berlin (1994)

  10. Herlihy M., Shavit N.: The Art of Multiprocessor Programming. Morgan Kaufmann Publishers, Los Altos (2008)

    Google Scholar 

  11. Hesselink W.H.: A challenge for atomicity verification. Sci. Comput. Program. 71, 57–72 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  12. Hesselink, W.H.: PVS proof scripts of “nonatomic bakery algorithm with bounded tokens”. Available at http://www.cs.rug.nl/~wim/mechver/bnonatomicMX/index.html (2009)

  13. Holzmann G.J.: The SPIN Model Checker, Primer and Reference Manual. Addison-Wesley, Reading (2004)

    Google Scholar 

  14. Inoue T., Hironaka T., Sasaki T., Fukae S., Koide T., Mattausch H.J.: Evaluation of bank-based multiport memory architecture with blocking network. Electron. Commun. Jpn 89, 498–510 (2006)

    Article  Google Scholar 

  15. Israeli A., Li M.: Bounded time-stamps. Distrib. Comput. 6, 205–209 (1993)

    Article  MATH  Google Scholar 

  16. Jayanti, P., Tan, K., Friedland, G., Katz, A.: Bounding Lamport’s Bakery algorithm. In: Proceedings of the SOFSEM, volume 2234 of LNCS, pp. 261–270 (2001)

  17. Katseff, H.P.: A new solution to the critical section problem. In: Tenth Annual ACM Symposium on Theory of Computing, pp. 86–88 (1978)

  18. Kessels J.L.W.: Arbitration without common modifiable variables. Acta Inf. 17, 135–141 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  19. Kim Y.J., Anderson J.H.: Nonatomic mutual exclusion with local spinning. Distrib. Comput. 19, 19–61 (2006)

    Article  Google Scholar 

  20. Lamport L.: A new solution of Dijkstra’s concurrent programming problem. Commun. ACM 17, 453–455 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  21. Lamport L.: The mutual exclusion problem—part I: a theory of interprocess communication, part II: statement and solutions. J. ACM 33, 313–348 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  22. Lamport L.: On interprocess communication. Parts I and II. Distrib. Comput. 1, 77–101 (1986)

    Article  MATH  Google Scholar 

  23. Lamport, L.: The mutual exclusion problem has been solved. Commun. ACM 34(1), 110,119 (1991)

    Google Scholar 

  24. Lamport L.: The temporal logic of actions. ACM Trans. Program. Lang. Syst. 16, 872–923 (1994)

    Article  Google Scholar 

  25. Lycklama E.A., Hadzilacos V.: A first-come-first-served mutual-exclusion algorithm with small communication variables. ACM Trans. Program. Lang. Syst. 13, 558–576 (1991)

    Article  Google Scholar 

  26. Owicki S., Gries D.: An axiomatic proof technique for parallel programs. Acta Inf. 6, 319–340 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  27. Owre, S., Shankar, N., Rushby, J.M., Stringer-Calvert, D.W.J.: PVS Version 2.4, System Guide, Prover Guide, PVS Language Reference. http://pvs.csl.sri.com (2001)

  28. Peterson G.L.: Myths about the mutual exclusion problem. Inf. Process. Lett. 12, 115–116 (1981)

    Article  MATH  Google Scholar 

  29. Peterson G.L.: A new solution to Lamport’s concurrent programming problem using small shared variables. ACM Trans. Program. Lang. Syst. 5(1), 56–65 (1983)

    Article  MATH  Google Scholar 

  30. Raynal M.: Algorithms for Mutual Exclusion. MIT Press, Cambridge (1986)

    MATH  Google Scholar 

  31. Shiue W.-T., Chakrabarti C.: Multi-module multi-port memory design for low power embedded systems. Design Autom. Embed. Syst. 9, 235–261 (2004)

    Article  Google Scholar 

  32. Takamura, M., Igarashi, Y.: Simple mutual exclusion algorithms based on bounded tickets on the asynchronous shared memory model. In: Proceedings of the COCOON, volume 2387 of LNCS, pp. 259–268 (2002)

  33. Taubenfeld, G.: The black-white bakery algorithm and related bounded-space, adaptive, local-spinning and FIFO algorithms. In: Proceedings of the DISC, volume 3274 of LNCS, pp. 56–70 (2004)

  34. Taubenfeld G.: Synchronization Algorithms and Concurrent Programming. Pearson Education/Prentice Hall, Englewood Cliffs (2006)

    Google Scholar 

  35. Vijayaraghavan, S.: A variant of the bakery algorithm with bounded values as a solution to Abraham’s concurrent programming problem. In: Proceedings of Design, Analysis and Simulation of Distributed Systems (2003)

  36. Vitányi, P.M.B.: Registers. In: Encyclopedia of Algorithms, pp. 761–764. Springer, Berlin (2008)

  37. Vitányi, P.M.B., Awerbuch, B.: Atomic shared register access by asynchronous hardware. In: 27th Annual Symposium on Foundations of Computer Science, pp. 233–243. IEEE, Los Alamitos, California, 1986. Corrigendum in 28th Annual Symposium on Foundations of Computer Science, p. 487. Los Angeles (1987)

  38. Woo T.-K.: A note on Lamport’s mutual exclusion algorithm. SIGOPS Oper. Syst. Rev. 24(4), 78–81 (1990)

    Article  Google Scholar 

  39. Zuo, W., Qi, Z., Jiaxing, L.: An intelligent multi-port memory. In: Proceedings of the IEEE International Symposium on Information Technology Application Workshops, pp. 251–254 (2008)

Download references

Author information

Authors and Affiliations

  1. Computer Science Program, University of Northern British Columbia, Prince George, BC, V2N4Z9, Canada

    Alex A. Aravind

  2. Department of Computing Science, University of Groningen, P.O. Box 407, 9700 AK, Groningen, The Netherlands

    Wim H. Hesselink

Authors
  1. Alex A. Aravind
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wim H. Hesselink
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alex A. Aravind.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aravind, A.A., Hesselink, W.H. Nonatomic dual bakery algorithm with bounded tokens. Acta Informatica 48, 67–96 (2011). https://doi.org/10.1007/s00236-011-0132-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00236-011-0132-0

Keywords

Search

Navigation