Abstract
Objects like queue, swap, and test-and-set allow two processes to reach consensus, and are consequently “universal” for a system of two processes. But are there deterministic objects that do not solve 2-process consensus, and nevertheless allow two processes to solve a task that is not otherwise wait-free solvable in read-write shared memory?
The answer “no” is a simple corollary of the main result of this paper: Let A be a deterministic object such that no protocol solves consensus among n + 1 processes using copies of A and read-write registers. If a task T is wait-free solvable by n + 1 processes using read-write shared-memory and copies of A, then T is also wait-free solvable when copies of A are replaced with n-consensus objects. Thus, from the task-solvability perspective, n-consensus is the second strongest object (after (n + 1)-consensus) in deterministic shared memory systems of n + 1 processes, i.e., there is a distinct gap between n- and (n + 1)-consensus.
We derive this result by showing that any (n + 1)-process protocol P that uses objects A can be emulated using only n-consensus objects. The resulting emulation is non-blocking and relies on an a priori knowledge of P. The emulation technique is another important contribution of this paper.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Fischer, M.J., Lynch, N.A., Paterson, M.S.: Impossibility of distributed consensus with one faulty process. Journal of the ACM 32(3), 374–382 (1985)
Herlihy, M.: Wait-free synchronization. ACM Transactions on Programming Languages and Systems 13(1), 124–149 (1991)
Herlihy, M., Shavit, N.: The topological structure of asynchronous computability. Journal of the ACM 46(6), 858–923 (1999)
Chandra, T.D., Hadzilacos, V., Jayanti, P., Toueg, S.: Generalized irreducibility of consensus and the equivalence of t-resilient and wait-free implementations of consensus. SIAM J. Comput. 34(2), 333–357 (2004)
Jayanti, P.: On the robustness of Herlihy’s hierarchy. In: Proceedings of the 12th Annual ACM Symposium on Principles of Distributed Computing (PODC), pp. 145–158 (August 1993)
Attiya, H., Welch, J.L.: Distributed Computing: Fundamentals, Simulations and Advanced Topics, 2nd edn. Wiley, Chichester (2004)
Borowsky, E., Gafni, E., Afek, Y.: Consensus power makes (some) sense! In: Proceedings of the 13th Annual ACM Symposium on Principles of Distributed Computing (PODC), pp. 363–372 (August 1994)
Neiger, G.: Failure detectors and the wait-free hierarchy. In: Proceedings of the 14th Annual ACM Symposium on Principles of Distributed Computing (PODC), pp. 100–109 (August 1995)
Ruppert, E.: The Consensus Power of Shared-Memory Distributed Systems. PhD thesis, University of Toronto (1999)
Loui, M.C., Abu-Amara, H.H.: Memory requirements for agreement among unreliable asynchronous processes. Advances in Computing Research, 163–183 (1987)
Dolev, D., Lynch, N.A., Pinter, S.S., Stark, E.W., Weihl, W.E.: Reaching approximate agreement in the presence of faults. J. ACM 33(3), 499–516 (1986)
Afek, Y., Weisberger, E., Weisman, H.: A completeness theorem for a class of synchronization objects (extended abstract). In: Proceedings of the 12th Annual ACM Symposium on Principles of Distributed Computing (PODC), pp. 159–170 (1993)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gafni, E., Kuznetsov, P. (2007). N-Consensus is the Second Strongest Object for N + 1 Processes. In: Tovar, E., Tsigas, P., Fouchal, H. (eds) Principles of Distributed Systems. OPODIS 2007. Lecture Notes in Computer Science, vol 4878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77096-1_19
Download citation
DOI: https://doi.org/10.1007/978-3-540-77096-1_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77095-4
Online ISBN: 978-3-540-77096-1
eBook Packages: Computer ScienceComputer Science (R0)