Common use of Lower Bounds Clause in Contracts

Lower Bounds. In order to formulate the strongest impossibility results related to Approximate Agreement in the Mobile Byzantine faults model we examine a weaker version of this problem referred in [11] as Simple Approximate Agreement. Each correct node has a real value from [0, 1] as input and chooses a real value. Correct behav- iors must satisfy the following properties: Agreement: The maximum difference between values chosen by correct nodes must be strictly smaller than the maximum difference between the inputs, or be equal to the latter difference if it is zero. Validity: Each correct node chooses a value in the range of the inputs of the nodes. We prove lower bounds for each Mobile Byzantine faults models: Garay’s (M1), Bonnet’s(M2), Sasaki’s (M3) and Burhman’s (M4). The bounds for the models (M3) and (M4) result from the classical bounds proved in [11] and the mapping defined in Section 3. In the case of models (M1) and (M2), since the behavior of cured processes cannot be totally controlled by the Byzantine adversary, specific proofs are needed.