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 the remaining (\(2^{2^n} -n\)) adversaries that might crash certain combination of processes and not others?
This paper presents a precise way to characterize such adversaries by introducing 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 how this notion enables to derive n equivalence classes of adversaries.
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References
Herlihy, M., Shavit, N.: The topological structure of asynchronous computability. J. ACM 46(6), 858–923 (1999)
Borowsky, E., Gafni, E.: Generalized flp impossibility result for t-resilient asynchronous computations. In: STOC, pp. 91–100 (1993)
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)
Fischer, M.J., Lynch, N.A., Paterson, M.S.: Impossibility of distributed consensus with one faulty process. J. ACM 32(2), 374–382 (1985)
Chaudhuri, S.: Agreement is harder than consensus: set consensus problems in totally asynchronous systems. In: PODC, pp. 311–324 (1990)
Borowsky, E., Gafni, E., Lynch, N.A., Rajsbaum, S.: The BG distributed simulation algorithm. Distributed Computing 14(3), 127–146 (2001)
Herlihy, M., Rajsbaum, S.: The decidability of distributed decision tasks (extended abstract). In: STOC, pp. 589–598 (1997)
Junqueira, F.P., Marzullo, K.: Designing algorithms for dependent process failures. In: Future Directions in Distributed Computing, pp. 24–28 (2003)
Fitzi, M., Maurer, U.M.: Efficient byzantine agreement secure against general adversaries. In: DISC, pp. 134–148 (1998)
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)
Zielinski, P.: Anti-Omega: the weakest failure detector for set agreement. In: PODC, pp. 55–64 (2008)
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. In: PODC, pp. 147–158 (1992)
Lo, W.K., Hadzilacos, V.: Using failure detectors to solve consensus in asynchronous shared-memory systems (extended abstract). In: WDAG, pp. 280–295 (1994)
Vitanyi, P.M.B., Awerbuch, B.: Atomic shared register access by asynchronous hardware. In: SFCS, Washington, DC, USA, pp. 233–243. IEEE Computer Society Press, Los Alamitos (1986)
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Delporte-Gallet, C., Fauconnier, H., Guerraoui, R., Tielmann, A. (2009). The Disagreement Power of an Adversary. In: Keidar, I. (eds) Distributed Computing. DISC 2009. Lecture Notes in Computer Science, vol 5805. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04355-0_6
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DOI: https://doi.org/10.1007/978-3-642-04355-0_6
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