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By Ivanyi A. (ed.)

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3. In the multicast service we provide two types of events, where qos denotes a quality of service required: mc-sendi (m, D, qos) : an event of processor pi which sends a message m together with its id to all processors in a destination set D ⊆ {0, . . , 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.

This lemma together with the before mentioned observations hence implies the following theorem. 13 The previous consensus algorithm solves the consensus problem in the presence of f crash failures in a message passing system in f + 1 rounds. The following theorem was rst proved by Fischer and Lynch for Byzantine failures. Dolev and Strong later extended it to crash failures. The theorem shows that the previous algorithm, assuming the given model, is optimal. 14 There is no algorithm which solves the consensus problem in less than f + 1 rounds in the presence of f crash failures, if n ≥ f + 2.

Our goal is to assign values of the logical clock to each instruction, so that these values appear to be readings of the global clock. That is, it possible to postpone or advance the instants when instructions are executed in such a way, that each instruction x that has been assigned a value tx of the logical clock, is executed exactly at the instant tx of the global clock, and that the resulting execution is a valid one, in the sense that it can actually occur when the algorithm is run with the modied delays.

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