Algorithms of informatics, vol.2.. applications (2007)(ISBN by Ivanyi A. (ed.)

By Ivanyi A. (ed.)

Ivanyi A. (ed.) Algorithms of informatics, vol.2.. purposes (2007)(ISBN 9638759623)

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Note that in the case of crash failures this validity condition is equivalent to requiring that every nonfaulty decision value is the input of some processor. Once a processor crashes it is of no interest to the algorithm, and no requirements are put on its decision. We begin by presenting a simple algorithm for consensus in a synchronous message passing system with crash failures. 4. 2. Consensus with crash failures Since the system is synchronous, an execution of the system consists of a series of rounds.

N − 1}. mc-recvi (m, j, qos) : an event of processor pi which receives a message m sent by processor pj . 13. Distributed Algorithms 624 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 dierent destination sets), then the messages received in each processors (if any) must be received in the same order as sent by the source.

We assume that each processor is given the same cut K = (k1 , . . , kn ) as an input. Then processors must determine a consistent cut K that is majorised by K . Each processor pi has an innite table V Ti [0, 1, 2, . ] of vectors. Processor executes instructions, and stores vector timestamps in consecutive entries of the table. Specically, entry m of the table is the vector timestamp V Ti [m] of the mth instruction executed by the processor; we dene V Ti [0] to be the zero vector. Processor pi begins calculating a cut right after the moment when the processor has executed instruction number ki .

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