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
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