Advertisement

Untangling Partial Agreement: Iterated x-consensus Simulations

  • Damien Imbs
  • Sergio Rajsbaum
  • Adrián Valle
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Asynchronous systems Consensus Distributed computing Iterated Immediate Snapshot Read/write shared memory Task solvability Wait-freedom 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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)CrossRefzbMATHGoogle Scholar
  2. 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. 3.
    Attiya, H., Bar-Noy, A., Dolev, D.: Sharing memory robustly in message-passing systems. J. ACM 42(1), 124–142 (1995)CrossRefzbMATHGoogle Scholar
  4. 4.
    Attiya, H., Welch, J.: Distributed Computing: Fundamentals, Simulations, and Advanced Topics. Synthesis Lectures on Distributed Computing Theory. Wiley (2004)Google Scholar
  5. 5.
    Biran, O., Moran, S., Zaks, S.: A combinatorial characterization of the distributed 1-solvable tasks. J. Algorithms 11(3), 420–440 (1990)CrossRefMathSciNetzbMATHGoogle Scholar
  6. 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. 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. 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. 9.
    Borowsky, E., Gafni, E., Lynch, N., Rajsbaum, S.: The BG distributed simulation algorithm. Distributed Computing 14(3), 127–146 (2001)CrossRefGoogle Scholar
  10. 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. 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) CrossRefGoogle Scholar
  12. 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)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Charron-Bost, B., Schiper, A.: The heard-of model: computing in distributed systems with benign faults. Distributed Computing 22(1), 49–71 (2009)CrossRefzbMATHGoogle Scholar
  14. 14.
    Chaudhuri, S.: More choices allow more faults: Set consensus problems in totally asynchronous systems. Inf. Comput. 105(1), 132–158 (1993)CrossRefzbMATHGoogle Scholar
  15. 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) CrossRefGoogle Scholar
  16. 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. 17.
    Chor, B., Nelson, L.-B.: Solvability in asynchronous environments II: Finite interactive tasks. SIAM J. Comput. 29(2), 351–377 (1999)CrossRefMathSciNetGoogle Scholar
  18. 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. 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. 20.
    Elrad, T., Francez, N.: Decomposition of distributed programs into communication-closed layers. Sci. Comput. Program. 2(3), 155–173 (1982)CrossRefzbMATHGoogle Scholar
  21. 21.
    Fischer, M.J., Lynch, N.A., Paterson, M.: Impossibility of distributed consensus with one faulty process. J. ACM 32(2), 374–382 (1985)CrossRefMathSciNetzbMATHGoogle Scholar
  22. 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. 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) CrossRefGoogle Scholar
  24. 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. 25.
    Gafni, E., Koutsoupias, E.: Three-processor tasks are undecidable. SIAM J. Comput. 28(3), 970–983 (1999)CrossRefMathSciNetzbMATHGoogle Scholar
  26. 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) CrossRefGoogle Scholar
  27. 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) CrossRefGoogle Scholar
  28. 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) CrossRefGoogle Scholar
  29. 29.
    Herlihy, M.: Wait-free synchronization. ACM Trans. Program. Lang. Syst. 13(1), 124–149 (1991)CrossRefGoogle Scholar
  30. 30.
    Herlihy, M., Kozlov, D., Rajsbaum, S.: Distributed Computing Through Combinatorial Topology. Morgan Kaufmann, Elsevier (2013)Google Scholar
  31. 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. 32.
    Herlihy, M., Rajsbaum, S.: A classification of wait-free loop agreement tasks. Theoretical Computer Science 291(1), 55–77 (2003)CrossRefMathSciNetzbMATHGoogle Scholar
  33. 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. 34.
    Herlihy, M., Rajsbaum, S.: The topology of distributed adversaries. Distributed Computing 26(3), 173–192 (2013)CrossRefzbMATHGoogle Scholar
  35. 35.
    Herlihy, M., Rajsbaum, S., Raynal, M.: Power and limits of distributed computing shared memory models. Theoretical Computer Science 509, 3–24 (2013)CrossRefMathSciNetzbMATHGoogle Scholar
  36. 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. 37.
    Herlihy, M., Shavit, N.: The topological structure of asynchronous computability. J. ACM 46(6), 858–923 (1999)CrossRefMathSciNetzbMATHGoogle Scholar
  38. 38.
    Herlihy, M., Wing, J.M.: Linearizability: A correctness condition for concurrent objects. ACM Trans. Program. Lang. Syst. 12(3), 463–492 (1990)CrossRefGoogle Scholar
  39. 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. 40.
    Neiger, G., Toueg, S.: Automatically increasing the fault-tolerance of distributed algorithms. J. Algorithms 11(3), 374–419 (1990)CrossRefMathSciNetzbMATHGoogle Scholar
  41. 41.
    Rajsbaum, S.: Iterated shared memory models. In: López-Ortiz, A. (ed.) LATIN 2010. LNCS, vol. 6034, pp. 407–416. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  42. 42.
    Rajsbaum, S., Raynal, M.: An introductory tutorial to concurrency-related distributed recursion. Bulletin of the EATCS, p. 111 (2013)Google Scholar
  43. 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)CrossRefMathSciNetGoogle Scholar
  44. 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) CrossRefGoogle Scholar
  45. 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) CrossRefGoogle Scholar
  46. 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. 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)CrossRefMathSciNetzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BremenBremenGermany
  2. 2.Instituto de MatemáticasUNAMCiudad de MexicoMexico
  3. 3.OracleZapopanMexico

Personalised recommendations