Easy impossibility proofs for distributed consensus problems
- 163 Downloads
Easy proofs are given, of the impossibility of solving several consensus problems (Byzantine agreement, weak agreement, Byzantine firing squad, approximate agreement and clock synchronization) in certain communication graphs.
It is shown that, in the presence ofm faults, no solution to these problems exists for communication graphs with fewer than 3m+1 nodes or less than 2m+1 connectivity. While some of these results had previously been proved, the new proofs are much simpler, provide considerably more insight, apply to more general models of computation, and (particularly in the case of clock synchronization) significantly strengthen the results.
Key wordsAgreement Distributed computing Fault tolerance
Unable to display preview. Download preview PDF.
- 1.Angluin D (1980) Local and global properties in networks of processors. Proceedings of the 12th STOC, April 30–May 2, 1980, Los Angeles, CA, pp 82–93Google Scholar
- 2.Burns J (1980) A formal model for message passing systems, TR-91, Indiana University, SeptGoogle Scholar
- 3.Burns J, Lynch N (1984) The byzantine firing squad problem, (submitted for publication)Google Scholar
- 4.Coan B, Dolev D, Dwork C, Stockmeyer L (1985) The distributed firing squad problem, Proceedings of the 17th STOC, May 6–8, 1985, Providence, RIGoogle Scholar
- 5.Dolev D (1982) The byzantine generals strike again. J Algorithms 3:14–30Google Scholar
- 6.Dolev D, Halpern J, Strong H (1984) On the possibility and impossibility of achieving clock synchronization. Proceedings of the 16th STOC, April 30–May 2, 1984, Washington, DC, pp 504–510Google Scholar
- 7.Dolev D, Lynch NA, Pinter S, Stark E, Weih W (1983) Reaching approximate agreement in the presence of faults, Proceedings of the 3rd Annual IEEE Symposium on Distributed Software and DatabasesGoogle Scholar
- 8.Itai A, Rodeh M (1981) The lord of the ring or probabilistic methods for breaking symmetry in distributive networks. RJ-3110. IBM Research Report AprilGoogle Scholar
- 9.Lamport L (1983) The weak byzantine general problem. JACM 30:668–676Google Scholar
- 10.Lamport L, Shostak R, Pease M (1982) The byzantine generals problem. ACM Trans Program Lang Syst 4:3 382–401Google Scholar
- 11.Mahaney S, Schneider F (1985) Inexact agreement: accuracy, precision, and graceful degradation, Proceedings of the 4th Annual ACM Symposium on Principles of Distributed Computing. August 5–7, 1985, Minacki, OntarioGoogle Scholar
- 12.Pease M, Shostak R, Lamport L (1980) Reaching agreement in the presence of faults. JACM 27:228–234Google Scholar