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

By Ivanyi A. (ed.)

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Extra resources for Algorithms of informatics, vol. 2

Example text

Recall that an execution is an interleaving of instructions of the n programs. Each instruction can be either a computational step of a processor, or sending a message, or receiving a message. Any instruction is performed at a distinct point of global time. However, the reading of the global clock is not available to processors. 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 modified delays.

All these arrays are initialised to store the value nil. For an array Xi of processor pi , we denote its jth entry by Xi [j] - intuitively this entry contains some information about processor pj . The array Rumor is used to store all the rumors that a processor knows. At the start, processor pi sets Rumorsi [i] to its own input rumori . 7. Rumor collection algorithms 629 value. The array Active is used to store a set of all the processors that the owner of the array knows as crashed. Once processor pi learns that some processor pj has failed, it immediately sets Activei [j] to failed.

But messages are received in the order they are sent, so pi processes before it processes . But then message arrives after snapshot was taken at pi . This is a desired contradiction. 5-1 Show that logical time preserves the happens before (

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