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Set Agreement Power Is Not a Precise Characterization for Oblivious Deterministic Anonymous Objects

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Structural Information and Communication Complexity (SIROCCO 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11639))

Abstract

Anonymous shared memory systems, recently introduced in [36], are composed of objects for which there is no a priori agreement between processes on their names. We resolve the following foundational open problems in theoretical distributed computing, for a model which includes both non-anonymous and anonymous shared objects: (1) Are non-trivial oblivious deterministic objects with the same set agreement power have the same computational power? (2) Is there a non-trivial oblivious deterministic object which is strictly weaker than an atomic read/write register? We prove that the answer to the first problem is negative, while the answer to the second problem is positive. The positive answer to the second problem implies that the common belief that every non-trivial deterministic object of consensus number one is at least as strong as atomic read/write registers is false. A noteworthy property of the proofs of our results lies in their simplicity.

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Notes

  1. 1.

    In [36], it is mentioned that anonymous registers are non-trivial objects which are strictly weaker than non-anonymous registers, when the number of processes is not a priori known. This statement is misleading. Indeed, it was proved in [36] that anonymous registers are strictly weaker than non-anonymous registers when the number of processes is not a priori known (or unbounded). However, it was not proved that anonymous registers are non-trivial objects for such a model.

References

  1. Afek, Y., Ellen, F., Gafni, E.: Deterministic objects: life beyond consensus. In: Proceedings of the ACM Symposium on Principles of Distributed Computing, PODC 2016, pp. 97–106 (2016)

    Google Scholar 

  2. Aghazadeh, Z., Imbs, D., Raynal, M., Taubenfeld, G., Woelfel, Ph.: Optimal memory-anonymous symmetric deadlock-free mutual exclusion. In: Proceedings of the ACM Symposium on Principles of Distributed Computing, PODC 2019 (2019)

    Google Scholar 

  3. Aspnes, J.: Randomized protocols for asynchronous consensus. Distrib. Comput. 16(2–3), 165–175 (2003)

    Article  Google Scholar 

  4. Borowsky, E., Gafni, E.: Generalized FLP impossibility result for \(t\)-resilient asynchronous computations. In: Proceedings of 25th ACM Symposium on Theory of Computing, pp. 91–100 (1993)

    Google Scholar 

  5. Buhrman, H., Panconesi, A., Silvestri, R., Vitanyi, P.: On the importance of having an identity or, is consensus really universal? Distrib. Comput. 18(3), 167–176 (2006)

    Article  Google Scholar 

  6. Chan, D.Y.C., Hadzilacos, V., Toueg, S.: Life beyond set agreement. In: Proceedings of the ACM Symposium on Principles of Distributed Computing, PODC 2017, pp. 345–354 (2017)

    Google Scholar 

  7. Chan, D.Y.C., Hadzilacos, V., Toueg, S.: On the number of objects with distinct power and the linearizability of set agreement objects. In: Proceedings of 31st International Symposium on Distributed Computing (DISC 2017), pp. 12:1–12:14 (2017)

    Google Scholar 

  8. Chan, D.Y.C., Hadzilacos, V., Toueg, S.: On the classification of deterministic objects via set agreement power. In: Proceedings of the ACM Symposium on Principles of Distributed Computing, PODC 2018, pp. 71–80 (2018)

    Google Scholar 

  9. Chandra, T., Hadzilacos, V., Jayanti, P., Toueg, S.: Wait-freedom vs. t-resiliency and the robustness of wait-free hierarchies. In: Proceedings of the 13th Annual ACM Symposium on Principles of Distributed Computing, PODC 1994, pp. 334–343 (1994)

    Google Scholar 

  10. Chaudhuri, S.: More choices allow more faults: set consensus problems in totally asynchronous systems. Inf. Comput. 105(1), 132–158 (1993)

    Article  MathSciNet  Google Scholar 

  11. Daian, E., Losa, G., Afek, Y., Gafni, E.: A wealth of sub-consensus deterministic objects. In: 32nd International Symposium on Distributed Computing, DISC 2018, pp. 17:1–17:17 (2018)

    Google Scholar 

  12. Delporte-Gallet, C., Fauconnier, H., Gafni, E., Kuznetsov, P.: Set-consensus collections are decidable. In: 20th International Conference on Principles of Distributed Systems (OPODIS 2016), pp. 7:1–7:15 (2017)

    Google Scholar 

  13. Delporte-Gallet, C., Fauconnier, H., Gafni, E., Rajsbaum, S.: Linear space bootstrap communication schemes. Theoret. Comput. Sci. 561, 122–133 (2015)

    Article  MathSciNet  Google Scholar 

  14. Godard, E., Imbs, D., Raynal, M., Taubenfeld, G.: Anonymous read/write memory: leader election and de-anonymization. In: Censor-Hillel, K., Flammini, M. (eds.) SIROCCO 2019. LNCS, vol. 11639, pp. 246–261. Springer, Cham (2019)

    Google Scholar 

  15. Herlihy, M.: Impossibility results for asynchronous pram. In: Proceedings of the 3rd Annual ACM Symposium on Parallel Algorithms and Architectures, pp. 327–336 (1991)

    Google Scholar 

  16. Herlihy, M., Rajsbaum, S., Raynal, M., Stainer, J.: From wait-free to arbitrary concurrent solo executions in colorless distributed computing. Theoret. Comput. Sci. 683, 1–21 (2017)

    Article  MathSciNet  Google Scholar 

  17. Herlihy, M., Ruppert, E.: On the existence of booster types. In: Proceedings of 41st IEEE Symposium on Foundations of Computer Science, FOCS 2000, pp. 653–663 (2000)

    Google Scholar 

  18. Herlihy, M.P.: Wait-free synchronization. ACM Trans. Program. Lang. Syst. 13(1), 124–149 (1991)

    Article  Google Scholar 

  19. Herlihy, M.P., Luchangco, V., Moir, M.: Obstruction-free synchronization: double-ended queues as an example. In: Proceedings of the 23rd International Conference on Distributed Computing Systems, p. 522 (2003)

    Google Scholar 

  20. Herlihy, M.P., Shavit, N.: The topological structure of asynchronous computability. J. ACM 46(6), 858–923 (1999)

    Article  MathSciNet  Google Scholar 

  21. Herlihy, M.P., Wing, J.M.: Linearizability: a correctness condition for concurrent objects. TOPLAS 12(3), 463–492 (1990)

    Article  Google Scholar 

  22. Jayanti, P.: On the robustness of Herlihy’s hierarchy. In: Proceedings of 12th ACM Symposium on Principles of Distributed Computing, PODC 1993, pp. 145–157 (1993)

    Google Scholar 

  23. Jayanti, P.: Robust wait-free hierarchies. J. ACM 44(4), 592–614 (1997)

    Article  MathSciNet  Google Scholar 

  24. Lamport, L.: On interprocess communication, parts I and II. Distrib. Comput. 1(2), 77–101 (1986)

    Article  MathSciNet  Google Scholar 

  25. Lo, W., Hadzilacos, V.: All of us are smarter than any of us: nondeterministic wait-free hierarchies are not robust. SIAM J. Comput. 30(3), 689–728 (2000)

    Article  MathSciNet  Google Scholar 

  26. Loui, M.C., Abu-Amara, H.: Memory requirements for agreement among unreliable asynchronous processes. Adv. Comput. Res. 4, 163–183 (1987)

    MathSciNet  Google Scholar 

  27. Pease, M., Shostak, R., Lamport, L.: Reaching agreement in the presence of faults. J. ACM 27(2), 228–234 (1980)

    Article  MathSciNet  Google Scholar 

  28. Rabin, M.O.: The choice coordination problem. Acta Informatica 17, 121–134 (1982)

    Article  MathSciNet  Google Scholar 

  29. Rachman, O.: Anomalies in the wait-free hierarchy. In: Tel, G., Vitányi, P. (eds.) WDAG 1994. LNCS, vol. 857, pp. 156–163. Springer, Heidelberg (1994). https://doi.org/10.1007/BFb0020431

    Chapter  Google Scholar 

  30. Rashid, S., Taubenfeld, G., Bar-Joseph, Z.: Genome wide epigenetic modifications as a shared memory consensus problem. In: The 6th Workshop on Biological Distributed Algorithms (BDA 2018), London, July 2018

    Google Scholar 

  31. Ruppert, E.: Determining consensus numbers. SIAM J. Comput. 30(4), 1156–1168 (2000)

    Article  MathSciNet  Google Scholar 

  32. Saks, M., Zaharoglou, F.: Wait-free \(k\)-set agreement is impossible: the topology of public knowledge. SIAM J. Comput. 29, 1449–1483 (2000)

    Article  MathSciNet  Google Scholar 

  33. Shavit, N., Taubenfeld, G.: The computability of relaxed data structures: queues and stacks as examples. Distrib. Comput. 29(5), 395–407 (2016)

    Article  MathSciNet  Google Scholar 

  34. Shenk, E.: The consensus hierarchy is not robust. In: Proceedings of 16th Annual ACM Symposium on Principles of Distributed Computing, PODC 1997, 279 p. (1997)

    Google Scholar 

  35. Taubenfeld, G.: Weak read/write registers. In: Frey, D., Raynal, M., Sarkar, S., Shyamasundar, R.K., Sinha, P. (eds.) ICDCN 2013. LNCS, vol. 7730, pp. 423–427. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-35668-1_29

    Chapter  Google Scholar 

  36. Taubenfeld, G.: Coordination without prior agreement. In: Proceedings of ACM Symposium on Principles of Distributed Computing, PODC 2017, pp. 325–334 (2017)

    Google Scholar 

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Authors and Affiliations

  1. The Interdisciplinary Center, P.O. Box 167, 46150, Herzliya, Israel

    Gadi Taubenfeld

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  1. Gadi Taubenfeld
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Correspondence to Gadi Taubenfeld .

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Editors and Affiliations

  1. Technion, Haifa, Israel

    Keren Censor-Hillel

  2. University of L'Aquila, L'Aquila, Italy

    Michele Flammini

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Taubenfeld, G. (2019). Set Agreement Power Is Not a Precise Characterization for Oblivious Deterministic Anonymous Objects. In: Censor-Hillel, K., Flammini, M. (eds) Structural Information and Communication Complexity. SIROCCO 2019. Lecture Notes in Computer Science(), vol 11639. Springer, Cham. https://doi.org/10.1007/978-3-030-24922-9_20

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  • DOI: https://doi.org/10.1007/978-3-030-24922-9_20

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  • Online ISBN: 978-3-030-24922-9

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