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hw6 - under 1 single crash fault reliable channels under an...

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CSE586 (Spring 2010): Homework 6 Due by Apr 21 Wednesday, in class. 1. (40 points) Consider the “synchronous agreement with crash faults” program we studied in Section 12.6. Modify this algorithm to design an early-stopping version of the algorithm that terminates within f 0 + 1 rounds, where f 0 , the actual number of crash faults, is less than f . Prove (argue for) the correctness of your algorithm. (Hint: Processes can track the other processes that failed, which is detectable by identi- fying the processes from which no message was received.) Answer: 2. (30 points) Prove or disprove whether the leader election problem (where all the nodes select the node with the highest id in the system as the leader) is solvable deterministically
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Unformatted text preview: under 1. single crash fault, reliable channels, under an asynchronous system model, 2. single crash fault, reliable channels, under synchronous system model, and 3. single crash fault, and undetectable message loss, under the synchronous model (Hint: Consider a reduction from the leader election problem to the consensus problem.) 3. (30 points) Consider Dijkstra’s stabilizing token ring problem. Recall that there were two actions. At process 0, we had: 0 .x = N.x-→ .x := 0 .x + 1 At all other processes j = 1 ..N , we had: j.x 6 = ( j-1) .x-→ j.x := ( j-1) .x Assume that x is an integer (unbounded). Provide a variant function and prove stabi-lization. 1...
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