The discovery, more than a decade ago, of the relation between Distributed-Computing (DC) and Algebraic-Topology (AT) raised the specter of requiring checking task solvability to be intimately connected to expertise in AT. Yet, in the area of Centralized Algorithms proving a problem to be NP or PSPACE complete requires more algorithmic expertise than complexity one. In analogy, we show that in DC the equivalent of polynomial-time reductions, is read-write reductions. We define the notion of read-write reduction between distributed tasks, and show that all interesting known read-write impossible tasks can be proven impossible via read-write reduction to a task called Symmetry-Breaking (SB). Discovering a read-write reduction requires solely algorithmic expertise.


Comparison Version Input Tuple Processor Output Output Tuple Latin American Symposium 
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  1. 1.
    Afek, Y., Attiya, H., Dolev, D., Gafni, E., Merrit, M., Shavit, N.: Atomic Snapshots of Shared Memory. In: Proc. 9th ACM Symposium on Principles of Distributed Computing (PODC 1990), pp. 1–13. ACM Press, New York (1990)CrossRefGoogle Scholar
  2. 2.
    Borowsky, E., Gafni, E.: Generalized FLP Impossibility Results for t-Resilient Asynchronous Computations. In: Proc. 25th ACM Symposium on the Theory of Computing (STOC 1993), pp. 91–100. ACM Press, New York (1993)CrossRefGoogle Scholar
  3. 3.
    Borowsky, E., Gafni, E.: Immediate Atomic Snapshots and Fast Renaming (Extended Abstract). In: Proc. 12th ACM Symposium on Principles of Distributed Computing (PODC 1993), pp. 41–51. ACM Press, New York (1993)CrossRefGoogle Scholar
  4. 4.
    Borowsky, E., Gafni, E.: A Simple Algorithmically Reasoned Characterization of Wait-Free Computations (Extended Abstract). In: Proc. 16th ACM Symposium on Principles of Distributed Computing (PODC 1997), pp. 189–198. ACM Press, New York (1997)CrossRefGoogle Scholar
  5. 5.
    Borowsky, E., Gafni, E., Lynch, N., Rajsbaum, S.: The BG Distributed Simulation Algorithm. Distributed Computing 14(3), 127–146 (2001)CrossRefGoogle Scholar
  6. 6.
    Chaudhuri, S.: More Choices Allow More Faults: Set Consensus Problems in Totally Asynchronous Systems. Information and Computation 105, 132–158 (1993)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Fischer, M.J., Lynch, N.A., Paterson, M.S.: Impossibility of Distributed Consensus with One Faulty Process. Journal of the ACM 32(2), 374–382 (1985)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Gafni, E.: DISC/GODEL presentation: R/WReductions, DISC 2004 (2004),
  9. 9.
    Afek, Y., Gafni, E., Rajsbaum, S., Raynal, M., Travers, C.: Simultaneous Consensus Tasks: A Tighter Characterization of Set-Consensus. In: Chaudhuri, S., Das, S.R., Paul, H.S., Tirthapura, S., et al. (eds.) ICDCN 2006. LNCS, vol. 4308, pp. 331–341. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  10. 10.
    Gafni, E.: Group-Solvability. In: Guerraoui, R. (ed.) DISC 2004. LNCS, vol. 3274, pp. 30–40. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  11. 11.
    Gafni, E., Kouznetsov, P.: Two Front Agreement with Application to Emulation and Robustness (to appear)Google Scholar
  12. 12.
    Attiya, H., Bar-Noy, A., Dolev, D., Peleg, D., Reischuk, R.: Renaming in an asynchronous environment. J. ACM 37(3), 524–548 (1990)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Fredrickson, N., Lynch, N.: Electing a Leader in a Synchronous Ring. J. ACM (January 1987)Google Scholar
  14. 14.
    Gafni, E., Rajsbaum, S.: Musical Benches. In: Fraigniaud, P. (ed.) DISC 2005. LNCS, vol. 3724, pp. 63–77. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  15. 15.
    Gafni, E., Rajsbaum, S., Herlihy, M.: 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
  16. 16.
    Gafni E., (in preparation)Google Scholar
  17. 17.
    Ostrovsky, R.: Private communication to the authorGoogle Scholar
  18. 18.
    Gafni, E., Rajsbaum, S., Raynal, M., Travers, C.: The Committee Decision Problem. In: Correa, J.R., Hevia, A., Kiwi, M. (eds.) LATIN 2006. LNCS, vol. 3887, pp. 502–514. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  19. 19.
    Herlihy, M.P.: Wait-Free Synchronization. ACM Transactions on programming Languages and Systems 11(1), 124–149 (1991)CrossRefGoogle Scholar
  20. 20.
    Herlihy, M.P., Shavit, N.: The Topological Structure of Asynchronous Computability. Journal of the ACM 46(6), 858–923 (1999)MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Saks, M., Zaharoglou, F.: Wait-Free k-Set Agreement is Impossible: The Topology of Public Knowledge. SIAM Journal on Computing 29(5), 1449–1483 (2000)MATHCrossRefMathSciNetGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Eli Gafni
    • 1
  1. 1.Department of Computer ScienceUCLALos AngelesUSA

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