By Ivanyi A. (ed.)

ISBN-10: 9638759623

ISBN-13: 9789638759627

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

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**Additional info for Algorithms of informatics, vol.2.. applications (2007)(ISBN 9638759623)**

**Example text**

For all k , the coordinate V T (x)[k] is at most the corresponding coordinate V T (y)[k]. We write x

Fault-tolerant consensus 609 taking two rounds. Each processor has a preferred decision for each phase, initially its input value. At the rst round of each phase, processors send their preferences to each other. Let vik be the majority value in the set of values received by processor pi at the end of the rst round of phase k . If no majority exists, a default value v⊥ is used. In the second round of the phase processor pk , called the king of the phase, sends its majority value vkk to all processors.

This problem is known as the two generals problem . Here two generals must coordinate an attack using couriers that may be destroyed by the enemy. It turns out that it is not possible to solve this problem using a nite 13. Distributed Algorithms 606 number of messages. We prove this fact by contradiction. Assume that there is a protocol used by processors A and B involving a nite number of messages. Let us consider such a protocol that uses the smallest number of messages, say k messages. Assume without loss of generality that the last k th message is sent from A to B .

### Algorithms of informatics, vol.2.. applications (2007)(ISBN 9638759623) by Ivanyi A. (ed.)

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