By Ivanyi A. (ed.)
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Post 12 months be aware: First released December twenty second 2005
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Extra resources for Algorithms of informatics, vol. 2
6. Communication services 621 Integrity: each message m received in event bc-recv has been sent in some bc-send event. No-Duplicates: each processor receives a message not more than once. Liveness: each message sent is received by all processors. In the model with failures we define the notion of reliable broadcast service, which satisfies Integrity, No-Duplicates and two kinds of Liveness properties: Nonfaulty Liveness: each message m sent by non-faulty processor pi must be received by every non-faulty processor.
Mc-recvi (m, j, qos) : an event of processor pi which receives a message m sent by processor pj . Note that the event mc-recv is similar to bc-recv. As in case of a broadcast service, we would like to provide useful ordering and reliable properties of the multicast services. We can adapt ordering requirements from the broadcast services. Basic Multicast does not require any ordering properties. Single-Source FIFO requires that if one processor multicasts messages (possibly to different destination sets), then the messages received in each processors (if any) must be received in the same order as sent by the source.
Rather the results mean that there are no algorithms that guarantee termination, agreement, and validity, in all executions. It is reasonable to assume that agreement and validity are essential, that is, if a consensus algorithm terminates, then agreement and validity are guaranteed. In fact there are efficient and useful algorithms for the consensus problem that are not guaranteed to terminate in all executions. In practice this is often sufficient because the special conditions that cause non-termination may be quite rare.