Enriching the basic Byzantine asynchronous model with a random coin Sample Clauses

Enriching the basic Byzantine asynchronous model with a random coin. As announced, the additional computational power used to solve ITB k-set agreement despite Byzantine processes is supplied by a multi-sided random coin denoted LRC. The random abstraction LRC provides each process with a local coin that provides it with a single operation denoted random(). Each invocation takes a finite set X as input parameter, and returns a value of X such that each value of X as the probability 1/|X| to be returned. As seen in the introduction, we assume k ≤ t. Moreover, we have also seen that, in order a correct process decides neither a value proposed only by Byzantine processes, nor a predefined default value, it is assumed that, whatever the domain of the values that can be proposed by the correct processes, in any execution, at most m different values are proposed by correct processes, where m depends on n and t, namely, n > m(t + 1). Finally, to rule out the trivial algorithm in which a correct process decides the value it proposes, we assume k < m. Hence, assuming the non-triviality conditions k < m and k ≤ t, and the fact that, in any execution, at most m different values are proposed by the correct processes, the system model considered here to solve the ITB k-set agreement problem is BAMPn,t[t < n/(m + 1), LRC].