2. (10 points) Suppose that we want to achieve Byzantine Consensus in a synchronous system, while satisfying the following properties, in addition to the termination property. Assume that each process has an input in the set {0,1,2,3}. • Validity: The decision (output) must equal the input of some non-faulty process. • Agreement: All non-faulty processes must reach the same decision (i.e, output). Does there exist a Byzantine Consensus algorithm for 4 processes that can tolerate 1 Byzantine failure? Answer YES or NO. If you answer NO, explain why.
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