Abstract
The condition based approach consists in identifying sets of input vectors, called conditions, for which it is possible to design a protocol solving a distributed computing problem despite failures. In a recent work we have applied the condition based approach to the interactive consistency (IC) problem (the agreement problem where the processes have to agree on the vector of proposed values), and provided a characterization of the conditions that allow us to solve it in presence of up to f c process crashes and f e erroneous proposals. We have shown that these conditions correspond exactly to error correcting codes, where the errors can be erasures or modified values. Here, we investigate this set of conditions from a complexity perspective, and show that it actually consists of a hierarchy of classes of conditions, \(\mathcal{E}^{[\delta]}_{f_c,f_e}\), where δ is the degree of the condition (0 ≤ δ ≤ f c ), each class being contained in the previous one (intuitively, the value f c -δ represents the “difficulty” of a class).
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References
Attiya, H., Welch, J.: Distributed Computing: Fundamentals, Simulations and Advanced Topics, p. 451. McGraw–Hill, New York (1998)
Ben-Or, M.: Another Advantage of Free Choice: Completely Asynchronous Agreement Protocols. In: Proc. 2nd ACM Symposium on Principles of Distributed Computing (PODC 1983), Montréal, pp. 27–30 (1983)
Chandra, T., Toueg, S.: Unreliable Failure Detectors for Reliable Distributed Systems. Journal of the ACM 43(2), 225–267 (1996)
Chaudhuri, S.: More Choices Allow More Faults: set Consensus Problems in Totally Asynchronous Systems. Information and Computation 105, 132–158 (1993)
Dwork, C., Lynch, N., Stockmeyer, L.: Consensus in the Presence of Partial Synchrony. Journal of the ACM 35(2), 288–323 (1988)
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)
Friedman, R., Mostefaoui, A., Rajsbaum, S., Raynal, M.: Distributed Agreement and its Relation with Error-Correcting Codes. In: Malkhi, D. (ed.) DISC 2002. LNCS, vol. 2508, pp. 63–87. Springer, Heidelberg (2002)
Garg, V.K.: Elements of Distributed Computing, p. 423. Wiley, Chichester (2002)
Hélary, J.-M., Hurfin, M., Mostéfaoui, A., Raynal, M., Tronel, F.: Computing Global Functions in Asynchronous Distributed Systems with Perfect Failure Detectors. IEEE Trans. on Parallel and Distributed Systems 11(9), 897–910 (2000)
Lynch, N.: Distributed Algorithms, p. 872. Morgan Kaufmann Pub., San Francisco (1996)
Mostefaoui, A., Rajsbaum, S., Raynal, M.: Conditions on Input Vectors for Consensus Solvability in Asynchronous Distributed Systems. In: Proc. 33rd ACM Symposium on Theory of Computing (STOC 2001), pp. 153–162. ACM Press, Hersonissos (2001)
Mostefaoui, A., Rajsbaum, S., Raynal, M., Roy, M.: A Hierarchy of Conditions for Consensus Solvability. In: Proc. 20th ACM Symposium on Principles of Distributed Computing (PODC 2001), pp. 151–160. ACM Press, Newport (2001)
Mostefaoui, A., Rajsbaum, S., Raynal, M., Roy, M.: Efficient Condition-Based Consensus. In: 8th Int. Colloquium on Structural Information and Communication Complexity (SIROCCO 2001), pp. 275–291. Carleton Univ. Press, Ottawa (2001)
Pease, L., Shostak, R., Lamport, L.: Reaching Agreement in Presence of Faults. Journal of the ACM 27(2), 228–234 (1980)
Powell, D.: Failures Mode Assumptions and Assumption Coverage. In: Proc. 22th IEEE Fault-Tolerant Computing Symposium (FTCS 1992), pp. 386–395. IEEE Society Press, Boston (1992)
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Mostefaoui, A., Rajsbaum, S., Raynal, M., Roy, M. (2003). A Hierarchy of Conditions for Asynchronous Interactive Consistency. In: Malyshkin, V.E. (eds) Parallel Computing Technologies. PaCT 2003. Lecture Notes in Computer Science, vol 2763. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45145-7_11
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DOI: https://doi.org/10.1007/978-3-540-45145-7_11
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