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On Set Consensus Numbers

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Distributed Computing (DISC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5805))

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Abstract

We propose a complete characterization of a large class of distributed tasks, with respect to a weakened solvability notion called weak termination. A task is weak-termination solvable if there is an algorithm by which at least one process outputs.

The proposed categorization of tasks is based on the weakest failure detectors needed to solve them. We show that every task \(\mathcal{T}\) in the considered class is equivalent (in the failure detector sense) to some form of set agreement, and thus its solvability with weak termination is completely characterized by its set consensus number: the maximal integer k such that \(\mathcal{T}\) can be (weak-termination) solved using read-write registers and k-set agreement objects.

The characterization goes through showing that \(\neg{\it \Omega}_k\), recently shown to be the weakest failure detector for the task of k-set agreement, is necessary to solve any task that is k-resilient impossible.

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References

  1. Chaudhuri, S.: Agreement is harder than consensus: Set consensus problems in totally asynchronous systems. In: PODC, pp. 311–324 (1990)

    Google Scholar 

  2. Herlihy, M., Shavit, N.: The asynchronous computability theorem for t-resilient tasks. In: STOC, pp. 111–120 (1993)

    Google Scholar 

  3. Saks, M., Zaharoglou, F.: Wait-free k-set agreement is impossible: The topology of public knowledge. In: STOC, pp. 101–110. ACM Press, New York (1993)

    Google Scholar 

  4. Borowsky, E., Gafni, E.: Generalized FLP impossibility result for t-resilient asynchronous computations. In: STOC, pp. 91–100. ACM Press, New York (1993)

    Google Scholar 

  5. Borowsky, E., Gafni, E., Lynch, N.A., Rajsbaum, S.: The BG distributed simulation algorithm. Distributed Computing 14(3), 127–146 (2001)

    Article  Google Scholar 

  6. Chandra, T.D., Toueg, S.: Unreliable failure detectors for reliable distributed systems. Journal of the ACM 43(2), 225–267 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  7. Chandra, T.D., Hadzilacos, V., Toueg, S.: The weakest failure detector for solving consensus. Journal of the ACM 43(4), 685–722 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  8. Jayanti, P., Toueg, S.: Every problem has a weakest failure detector. In: PODC, pp. 75–84 (2008)

    Google Scholar 

  9. Gafni, E., Kuznetsov, P.: The weakest failure detector for solving k-set agreement. In: PODC (2009), http://www.net.t-labs.tu-berlin.de/~petr/pubs/wfd-kset.pdf

  10. Delporte-Gallet, C., Fauconnier, H., Guerraoui, R., Tielmann, A.: The disagreement power of an adversary (brief announcement). In: PODC (2009)

    Google Scholar 

  11. Gafni, E., Guerraoui, R.: Simulating few by many: Limited concurrency=set consensus. Unpublished manuscript (2009), http://www.cs.ucla.edu/~eli/eli/kconc.pdf

  12. Zieliński, P.: Automatic classification of eventual failure detectors. In: Pelc, A. (ed.) DISC 2007. LNCS, vol. 4731, pp. 465–479. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  13. Zieliński, P.: Anti-omega: the weakest failure detector for set agreement. In: PODC (2008)

    Google Scholar 

  14. Gafni, E.: The extended BG-Simulation. In: STOC (2009), http://www.cs.ucla.edu/~eli/eli/230-gafni1.pdf

  15. Lo, W.K., Hadzilacos, V.: Using failure detectors to solve consensus in asynchronous shared memory systems. In: Tel, G., Vitányi, P.M.B. (eds.) WDAG 1994. LNCS, vol. 857, pp. 280–295. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  16. Guerraoui, R., Kuznetsov, P.: Failure detectors as type boosters. Distributed Computing 20(5), 343–358 (2008)

    Article  MATH  Google Scholar 

  17. Anta, A.F., Rajsbaum, S., Travers, C.: Weakest failure detectors via an egg-laying simulation (brief announcement). In: PODC (2009)

    Google Scholar 

  18. Herlihy, M.: Wait-free synchronization. ACM Transactions on Programming Languages and Systems 13, 123–149 (1991)

    Article  Google Scholar 

  19. Delporte-Gallet, C., Fauconnier, H., Guerraoui, R.: (Almost) all objects are universal in message passing systems. In: Fraigniaud, P. (ed.) DISC 2005. LNCS, vol. 3724, pp. 184–198. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Computer Science Department, University of California, Los Angeles, USA

    Eli Gafni

  2. Deutsche Telekom Laboratories, TU Berlin, Berlin, Germany

    Petr Kuznetsov

Authors
  1. Eli Gafni
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  2. Petr Kuznetsov
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, The Technion – Israel Institute of Technology, 32000, Haifa, Israel

    Idit Keidar

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© 2009 Springer-Verlag Berlin Heidelberg

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Gafni, E., Kuznetsov, P. (2009). On Set Consensus Numbers. In: Keidar, I. (eds) Distributed Computing. DISC 2009. Lecture Notes in Computer Science, vol 5805. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04355-0_8

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  • DOI: https://doi.org/10.1007/978-3-642-04355-0_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04354-3

  • Online ISBN: 978-3-642-04355-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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