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a) Show that the Srikanth-Toueg algorithm has skew at most d + u.

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Exercise 4: Fault Frustration

Task 1: I’m Getting Tired of these Delays!

a) Show that the Srikanth-Toueg algorithm has skew at most d + u.

b) Show that this skew bound is tight. It suffices to do so for the maximal number of faults dn/3e − 1.

Task 2: Stop Failing and Start Synchronizing!

In this exercise, 3f ≥ n, i.e., there may be “too many” Byzantine nodes.

a) Show that clock synchronization is impossible with this many faults if the constant amortized progress condition is satisfied. (Hint: First “spend” some of the uncer- tainty and clock drifts to show that logical clocks cannot increase too rapidly. Then argue that any solution would imply a pulse synchronization algorithm.)

b) Show that even with this many faults, there is an algorithm that achieves constant skew and has unbounded logical clocks. You may assume that max

v∈Vg

{H

v

(0)} ≤ H ∈ R

+

. (Hint: Solve the problem without communication!)

c) Is the solution from b) useful? (Remark: This is an open-ended discussion. There is

not necessarily a single right answer.)

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