Correctness of OGBA Sample Clauses

Correctness of OGBA. In order to prove the correctness of the proposed protocol, a vertex µ is called common if each fault-free node has the same value of µ [7]. That is, if vertex µ is common, then the value stored in vertex µ of each fault-free node’s mg-tree or ic-tree is identical. When each fault-free node has a common initial value of the source node in the root of an ic-tree, and if the root s of an ic-tree in a fault-free node is common and the initial value received from the source node is stored in the root of the tree structure, then agreement is reached because the root is common. Thus, the constraints, (Agreement) and (Validity), can be rewritten as: Agreement’: root s is common, and Validity’: VOTE(s) = vs for each fault-free node, if the source node is fault-free. To prove that a vertex is common, the term common frontier is defined as follows: When every root-to-leaf path of the tree (an mg-tree or an ic-tree) contains a common vertex, the collection of common vertices forms a common frontier [7]. In other words, every fault-free node has identical messages collected in the common frontier if a common frontier exists in a fault-free node’s tree structure (mg-tree or ic-tree). Subsequently, using the same majority voting function to compute the root value of the tree structure, every fault-free node can compute the same root value because they have used the same input (the same collected messages in the common frontier). The same computing function causes the same output (the root value). Since OGBA can solve the BA problem, the correctness of OGBA should be examined in the following two ways:
Sample 1
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Related to Correctness of OGBA

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