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For example, pro *Lcesses  p 1  and  p 2  can block  p 3  forever if  p 3  arrives second and  p 1  and  p 2  cycle alternately through their critical UU@ sections.  zConsider a binary tree with  n  leaves, one for each process. Each internal node has an associated semaphore. The 0zprocesses desiring to enter their critical sections perform  down  operations on successive semaphores from their leaves to the root of the tree, execute their critical section, and perform  up  operations in reverse order back down @ the tree. 1`3Show this scheme implements safe mutual exclusion. !2 pDiscuss how the shape of the binary tree can affect the relative speeds of the processes and enforce a priority @scheme.  nThis problem asks you to apply a modification of Havenders ordered resource policy to processes, rather than 0oresources. Given that the mutual exclusion, hold and wait, and no preemption conditions are in place, consider qthe following strategy: All processes are given unique priorities. When more than one process is waiting for a qresource and the resource becomes available, allocate the resource to the waiting process with the highest prior@oity. Either prove this prevents deadlock or give an example in which this strategy does not prevent deadlock. % kUse Holts graph-based model to prove that the collective requests policy, in which a process requests and 1@?acquires all its needed resources at once, prevents deadlock. 4@`OProve that Maekawas distributed mutual exclusion algorithm prevents deadlock. A5`wShow that Byzantine agreement cannot always be reached among four processors when  two  processors are faulty. HHˆ;6HHˆ66 lH$ @5!:H$ 99l H$ @6!H$ 8Wl6March 14, 2000ECS 251 Winter 2000Page  1  HUV @7!8HHUV GGl}? B@<? GW8e }?H B;=?H GW9e- }H B<H GW:e }? BK?? HW;e }?H B>@?H HW<e-- }H B?;H HW=e }? BNJ? 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