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Symposium on Self-Stabilizing Systems

SSS 2015: Stabilization, Safety, and Security of Distributed Systems pp 139–155Cite as

Untangling Partial Agreement: Iterated x-consensus Simulations

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9212))

Abstract

The basic read/write shared memory model where asynchronous and crash prone processes communicate to solve a task is difficult to analyze. A more structured model is the iterated immediate snapshot model (IIS), where processes execute communication closed rounds. In each round, they communicate using read/write registers that cannot be reused in later rounds. It is known that a task is solvable in the IIS model if and only if it is solvable in the basic read/write model. Both models are also equivalent when, in addition to read/write registers, processes also have access to stronger communication objects called 01-tasks.

This paper extends further the task computability equivalence presenting a simulation that includes x-consensus objects, which solve consensus among up to x processes. The simulation implies that an iterated model where processes communicate through a sequence consisting only of x-consensus objects is equivalent to the basic shared memory model augmented with x-consensus objects.

S. Rajsbaum—Partially supported by a UNAM-PAPIIT grant.

D. Imbs and A. Valle—Part of this work was done while the authors were at the Instituto de Matemáticas, UNAM.

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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)

    Article  MATH  Google Scholar 

  2. Afek, Y., Weisberger, E., Weisman, H.: A completeness theorem for a class of synchronization objects. In: Proceedings of the 12th ACM Symposium on Principles of Distributed Computing, PODC 1993, pp. 159–170. ACM (1993)

    Google Scholar 

  3. Attiya, H., Bar-Noy, A., Dolev, D.: Sharing memory robustly in message-passing systems. J. ACM 42(1), 124–142 (1995)

    Article  MATH  Google Scholar 

  4. Attiya, H., Welch, J.: Distributed Computing: Fundamentals, Simulations, and Advanced Topics. Synthesis Lectures on Distributed Computing Theory. Wiley (2004)

    Google Scholar 

  5. Biran, O., Moran, S., Zaks, S.: A combinatorial characterization of the distributed 1-solvable tasks. J. Algorithms 11(3), 420–440 (1990)

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  7. Borowsky, E., Gafni, E.: Immediate atomic snapshots and fast renaming. In: Proc. of the 12th ACM Symp. on Principles of Dist. Computing, PODC 1993, pp. 41–51. ACM (1993)

    Google Scholar 

  8. Borowsky, E., Gafni, E.: A simple algorithmically reasoned characterization of wait-free computation (extended abstract). In: Proceedings of the 16th ACM Symposium on Principles of Distributed Computing, PODC 1997, pp. 189–198. ACM (1997)

    Google Scholar 

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

    Article  Google Scholar 

  10. Bouzid, Z., Gafni, E., Kuznetsov, P.: Strong equivalence relations for iterated models. In: Aguilera, M.K., Querzoni, L., Shapiro, M. (eds.) OPODIS 2014. LNCS, vol. 8878, pp. 139–154. Springer, Heidelberg (2014)

    Google Scholar 

  11. Castañeda, A., Imbs, D., Rajsbaum, S., Raynal, M.: Renaming is weaker than set agreement but for perfect renaming: a map of sub-consensus tasks. In: Fernández-Baca, D. (ed.) LATIN 2012. LNCS, vol. 7256, pp. 145–156. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  12. Chandra, T., Hadzilacos, V., Jayanti, P., Toueg, S.: Generalized irreducibility of consensus and the equivalence of t-resilient and wait-free implementations of consensus. SIAM Journal on Computing 34(2), 333–357 (2005)

    Article  MathSciNet  Google Scholar 

  13. Charron-Bost, B., Schiper, A.: The heard-of model: computing in distributed systems with benign faults. Distributed Computing 22(1), 49–71 (2009)

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  15. Chaudhuri, S., Reiners, P.: Understanding the set consensus partial order using the borowsky-gafni simulation. In: Babaoğlu, Ö., Marzullo, K. (eds.) WDAG 1996. LNCS, vol. 1151, pp. 362–379. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  16. Chor, B., Moscovici, L.: Solvability in asynchronous environments. In: Proc. of the 30th Annual Symposium on Foundations of Computer Science, FOCS 1989, pp. 422–427 (1989)

    Google Scholar 

  17. Chor, B., Nelson, L.-B.: Solvability in asynchronous environments II: Finite interactive tasks. SIAM J. Comput. 29(2), 351–377 (1999)

    Article  MathSciNet  Google Scholar 

  18. Chou, C.T., Gafni, E.: Understanding and verifying distributed algorithms using stratified decomposition. In: Proceedings of the 7th ACM Symposium on Principles of Distributed Computing, PODC 1988, pp. 44–65. ACM (1988)

    Google Scholar 

  19. Conde, R., Rajsbaum, S.: The complexity gap between consensus and safe-consensus. In: Halldórsson, M.M. (ed.) SIROCCO 2014. LNCS, vol. 8576, pp. 68–82. Springer, Heidelberg (2014)

    Google Scholar 

  20. Elrad, T., Francez, N.: Decomposition of distributed programs into communication-closed layers. Sci. Comput. Program. 2(3), 155–173 (1982)

    Article  MATH  Google Scholar 

  21. Fischer, M.J., Lynch, N.A., Paterson, M.: Impossibility of distributed consensus with one faulty process. J. ACM 32(2), 374–382 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  22. Gafni, E.: Round-by-round fault detectors (extended abstract): unifying synchrony and asynchrony. In: Proceedings of the 17th ACM Symposium on Principles of Distributed Computing, PODC 1998, pp. 143–152. ACM (1998)

    Google Scholar 

  23. Gafni, E.: The 0–1-exclusion families of tasks. In: Baker, T.P., Bui, A., Tixeuil, S. (eds.) OPODIS 2008. LNCS, vol. 5401, pp. 246–258. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  24. Gafni, E., Herlihy, M.: Sporadic solutions to zero-one exclusion tasks. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds.) ICALP 2014. LNCS, vol. 8572, pp. 1–10. Springer, Heidelberg (2014)

    Google Scholar 

  25. Gafni, E., Koutsoupias, E.: Three-processor tasks are undecidable. SIAM J. Comput. 28(3), 970–983 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  26. Gafni, E., Rajsbaum, S.: Distributed programming with tasks. In: Lu, C., Masuzawa, T., Mosbah, M. (eds.) OPODIS 2010. LNCS, vol. 6490, pp. 205–218. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  27. Gafni, E., Rajsbaum, S.: Recursion in distributed computing. In: Dolev, S., Cobb, J., Fischer, M., Yung, M. (eds.) SSS 2010. LNCS, vol. 6366, pp. 362–376. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  28. Gafni, E., Rajsbaum, S., Herlihy, M.P.: Subconsensus tasks: renaming is weaker than set agreement. In: Dolev, S. (ed.) DISC 2006. LNCS, vol. 4167, pp. 329–338. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

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

    Article  Google Scholar 

  30. Herlihy, M., Kozlov, D., Rajsbaum, S.: Distributed Computing Through Combinatorial Topology. Morgan Kaufmann, Elsevier (2013)

    Google Scholar 

  31. Herlihy, M., Rajsbaum, S.: The decidability of distributed decision tasks (extended abstract). In: Proceedings of the 29th ACM Symposium on Theory of Computing, STOC 1997, pp. 589–598. ACM (1997)

    Google Scholar 

  32. Herlihy, M., Rajsbaum, S.: A classification of wait-free loop agreement tasks. Theoretical Computer Science 291(1), 55–77 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  33. Herlihy, M., Rajsbaum, S.: Simulations and reductions for colorless tasks. In: Proc. of the 31st ACM Symp. on Principles of Dist. Computing, PODC 2012, pp. 253–260. ACM (2012)

    Google Scholar 

  34. Herlihy, M., Rajsbaum, S.: The topology of distributed adversaries. Distributed Computing 26(3), 173–192 (2013)

    Article  MATH  Google Scholar 

  35. Herlihy, M., Rajsbaum, S., Raynal, M.: Power and limits of distributed computing shared memory models. Theoretical Computer Science 509, 3–24 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  36. Herlihy, M., Rajsbaum, S., Tuttle, M.R.: Unifying synchronous and asynchronous message-passing models. In: Proceedings of the 17th ACM Symposium on Principles of Distributed Computing, PODC 1998, pp. 133–142. ACM (1998)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  39. Imbs, D., Raynal, M.: The multiplicative power of consensus numbers. In: Proc. of the 29th ACM Symp. on Principles of Dist. Computing, PODC 2010, pp. 26–35. ACM (2010)

    Google Scholar 

  40. Neiger, G., Toueg, S.: Automatically increasing the fault-tolerance of distributed algorithms. J. Algorithms 11(3), 374–419 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  41. Rajsbaum, S.: Iterated shared memory models. In: López-Ortiz, A. (ed.) LATIN 2010. LNCS, vol. 6034, pp. 407–416. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  42. Rajsbaum, S., Raynal, M.: An introductory tutorial to concurrency-related distributed recursion. Bulletin of the EATCS, p. 111 (2013)

    Google Scholar 

  43. Rajsbaum, S., Raynal, M., Travers, C.: An impossibility about failure detectors in the iterated immediate snapshot model. Inf. Process. Lett. 108(3), 160–164 (2008)

    Article  MathSciNet  Google Scholar 

  44. Rajsbaum, S., Raynal, M., Travers, C.: The iterated restricted immediate snapshot model. In: Hu, X., Wang, J. (eds.) COCOON 2008. LNCS, vol. 5092, pp. 487–497. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  45. Raynal, M., Stainer, J.: Increasing the power of the iterated immediate snapshot model with failure detectors. In: Even, G., Halldórsson, M.M. (eds.) SIROCCO 2012. LNCS, vol. 7355, pp. 231–242. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  46. Raynal, M., Stainer, J.: Synchrony weakened by message adversaries vs asynchrony restricted by failure detectors. In: Proceedings of the 2013 ACM Symposium on Principles of Distributed Computing, PODC 2013, pp. 166–175. ACM (2013)

    Google Scholar 

  47. Saks, M.E., Zaharoglou, F.: Wait-free k-set agreement is impossible: The topology of public knowledge. SIAM J. Comput. 29(5), 1449–1483 (2000)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Bremen, 28334, Bremen, Germany

    Damien Imbs

  2. Instituto de Matemáticas, UNAM, D.F. 04510, Ciudad de Mexico, Mexico

    Sergio Rajsbaum

  3. Oracle, Zapopan, Jalisco, Mexico

    Adrián Valle

Authors
  1. Damien Imbs
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  2. Sergio Rajsbaum
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  3. Adrián Valle
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Correspondence to Damien Imbs .

Editor information

Editors and Affiliations

  1. Université du Québec en Outaouais, Gatineau, QC, Canada

    Andrzej Pelc

  2. University of Connecticut, Storrs, Connecticut, USA

    Alexander A. Schwarzmann

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Imbs, D., Rajsbaum, S., Valle, A. (2015). Untangling Partial Agreement: Iterated x-consensus Simulations. In: Pelc, A., Schwarzmann, A. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2015. Lecture Notes in Computer Science(), vol 9212. Springer, Cham. https://doi.org/10.1007/978-3-319-21741-3_10

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  • DOI: https://doi.org/10.1007/978-3-319-21741-3_10

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