Abstract
At the heart of distributed computing lies the fundamental result that the level of agreement that can be obtained in an asynchronous shared memory model where t processes can crash is exactly t + 1. In other words, an adversary that can crash any subset of size at most t can prevent the processes from agreeing on t values. But what about all the other \({2^{2^n - 1} - (n+1)}\) adversaries that are not uniform in this sense and might crash certain combination of processes and not others? This paper presents a precise way to classify all adversaries. We introduce the notion of disagreement power: the biggest integer k for which the adversary can prevent processes from agreeing on k values. We show how to compute the disagreement power of an adversary and derive n equivalence classes of adversaries.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Afek Y., Attiya H., Dolev D., Gafni E., Merritt M., Shavit N.: Atomic snapshots of shared memory. J. ACM 40(4), 873–890 (1993)
Ashwinkumar, B.V., Patra, A., Choudhary, A., Srinathan, K., Rangan, C.P.: On tradeoff between network connectivity, phase complexity and communication complexity of reliable communication tolerating mixed adversary. In: PODC, pp. 115–124 (2008)
Borowsky, E., Gafni, E.: Generalized FLP impossibility result for t-resilient asynchronous computations. In: STOC, pp. 91–100 (1993)
Borowsky E., Gafni E., Lynch N.A., Rajsbaum S.: The BG distributed simulation algorithm. Distrib. Comput. 14(3), 127–146 (2001)
Chaudhuri S.: More choices allow more faults: set consensus problems in totally asynchronous systems. Inf. Comput. 105(1), 132–158 (1993)
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)
Chandra T.D., Hadzilacos V., Toueg S.: The weakest failure detector for solving consensus. J. ACM 43(4), 685–722 (1996)
Chandra T.D., Toueg S.: Unreliable failure detectors for reliable distributed systems. J. ACM 43(2), 225–267 (1996)
Fischer M.J., Lynch N.A., Paterson M.S.: Impossibility of distributed consensus with one faulty process. J. ACM 32(2), 374–382 (1985)
Fitzi, M., Maurer, U.M.: Efficient byzantine agreement secure against general adversaries. In: DISC, pp. 134–148 (1998)
Herlihy, M., Rajsbaum, S.: The decidability of distributed decision tasks (extended abstract). In: STOC, pp. 589–598 (1997)
Herlihy M., Shavit N.: The topological structure of asynchronous computability. J. ACM 46(6), 858–923 (1999)
Junqueira F., Marzullo K.: A framework for the design of dependent-failure algorithms. Concurr. Comput. Pract. Exp. 19(17), 2255–2269 (2007)
Lo, W.-K., Hadzilacos, V.: Using failure detectors to solve consensus in asynchronous shared-memory systems (extended abstract). In: WDAG, pp. 280–295 (1994)
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)
Vitányi, P.M.B., Awerbuch, B.: Atomic shared register access by asynchronous hardware (detailed abstract). In: FOCS, pp. 233–243 IEEE (1986)
Zielinski P.: Anti-Omega: the weakest failure detector for set agreement. Distrib Comput 22(5–6), 335–348 (2010)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Delporte-Gallet, C., Fauconnier, H., Guerraoui, R. et al. The disagreement power of an adversary. Distrib. Comput. 24, 137–147 (2011). https://doi.org/10.1007/s00446-010-0122-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00446-010-0122-4