Another way to generalize the two-thread Peterson lock is to arrange a number of two-thread Peterson locks in a binary tree. Suppose n is a power of two. Each thread is assigned a leaf lock which it...

Another way to generalize the two-thread Peterson lock is to arrange a number of two-thread Peterson locks in a binary tree. Suppose n is a power of two. Each thread is assigned a leaf lock which it shares with one other thread. Each lock treats one thread as thread 0 and the other as thread 1.In the tree-lock’s acquire method, the thread acquires every two-thread Peterson lock from that thread’s leaf to the root. The tree-lock’s release method for the tree-lock unlocks each of the two-thread Peterson locks that thread has acquired, from the root back to its leaf. At any time, a thread can be delayed for a finite duration. (In other words, threads can take naps, or even vacations, but they do not drop dead.)For each of the following properties, either sketch a proof that it holds, or describe a(possibly infinite) execution where it is violated:

1. mutual exclusion,

2. freedom from deadlock,

3.freedom from starvation.

Is there an upper bound on the number of times the tree-lock can be acquired and released between the time a thread starts acquiring the tree-lock and when it succeeds?