A Simple Command History Sample Clauses

A Simple Command History. ‌ Using Multicoordinated Paxos to solve Generic Broadcast is straightforward, and is more related to choosing the right c-struct than changing the protocol. In fact, the only change is restricting the use of c-structs in the protocol to c-hists. In this section we define a simple representation of c-hists and the operations performed on it. Command histories can be represented as sequences of commands. The com- mand history a⊥, for example, may be represented simply as 〈〉, while the command history ⊥ b d , where the arrows point to the previous elements in the par- 〈 〉 〈 〉 〈 〉 〈 〉 tial order, may be represented as a, b, c, d , a, c, b, d , a, b, d , c , b, a, d , c , or 〈 〉 b, a, c, d . ≤ ≤ | | This representation, which is in fact a topological sorting of the c-hist, ensures that, given a command history (S , ), integers i and j , i < j < S , and the sequence s that represents the command history, s[i ] s[j ]. • New commands can be added to a sequence by simply appending it at the se- quence’s end, if it is not in the sequence yet. Formally, the operator can be defined as follows: 〈C , . . . , C 〉 • C = . 〈C1, . . . , Cm 〉 if ∃i , C = Ci 1 m 〈C1, . . . , Cm , C 〉 otherwise. = Because these sequences do not represent all the ordering information, the con- flict relation ( ) is still needed to assess the order of commands within sequences when, for example, calculating the lub or checking the compatibility. H \ Algorithm 8 below determines the longest common prefix between two com- mand histories H and I , that is H I . It does so by checking if the head h of H exists on I before any conflicting command, in which case it is part of their common prefix. Otherwise, the algorithm recursively proceeds on the tail of H stripped of the descendants of h, since none of them can be part of the prefix. Observe that in this definition we use the set minus operator, , to remove some element from a sequence. ∆ Algorithm 8 Longest common prefix of two c-hists H and I .
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