By Ivanyi A. (ed.)

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

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

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This question can be answered through a generalisation of the Logical-Clock algorithm presented earlier. This generalisation is called vector clocks. The Vector-Clocks algorithm allows processors to relate instructions, and this relation is exactly the happens before relation. Each processor pi maintains a vector Vi of n integers. The j -th coordinate of the vector is denoted by Vi [j]. The vector is initialised to the zero vector (0, . . , 0). A vector is modied each time processor executes an instruction, in a way similar to the way counter was modied in the Logical-Clock algorithm.

3. Consensus with Byzantine failures In a computation step of a faulty processor in the Byzantine model, the new state of the processor and the message sent are completely unconstrained. As in the reliable case, every processor takes a computation step in every round and every message sent is delivered in that round. Hence a faulty processor can behave arbitrarily and even maliciously. For example, it could send dierent messages to dierent processors. It can even appear that the faulty processors coordinate with each other.

Case 2. Triple (m, t, k) (without loss of generality) is accepted by processor pi before triple (m , t , l) is pending. If (t, k) < (t , l) then still the acceptance is according to the order of (t, k), (t , l). Otherwise (t, k) > (t , l), and by condition in line 43 we get in particular that t ≤ T [l], and consequently t ≤ T [l]. This can not happen because of the ssf requirement and the assumption that processor pi has not yet received message < m , t > from l via the ssf broadcast service. Now we address reliable versions of Causal Order and Total Order services.

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