OS Process Management

void P (binary_semaphore *s) {
  unsigned y;
  unsigned *x = &(s->value);
  do {
     fetch-and-set x, y;
  } while (y);
}

void V (binary_semaphore *s) {
  S->value = 0;
}

Process X:                         Process Y:
private i;                         private i;
for (i=0; i < n; i++) {            for (i=0; i < n; i++) {
   a[i] = f(i);                       EntryY(R, S);
   ExitX(R, S);                       b[i]=g(a[i]);
}                                 }

ExitX(R, S) {
  P(R);
  V(S);
}

EntryY (R, S) {
  P(S);
  V(R);
}

ExitX(R, S) {
  V(R);
  V(S);
}

EntryY(R, S) {
  P(R);
  P(S);
}

ExitX(R, S) {
  P(S);
  V(R);
}
EntryY(R, S) {
  V(S);
  P(R);
}

ExitX(R, S) {
  V(R);
  P(S);
}
EntryY(R, S) {
  V(S);
  P(R);
}

Three concurrent processes X, Y, and Z execute three different code segments that access and update certain shared variables. Process X executes the P operation (i.e., wait) on semaphores a, b and c; process Y executes the P operation on semaphores b, c and d; process Z executes the P operation on semaphores c, d, and a before entering the respective code segments. After completing the execution of its code segment, each process invokes the V operation (i.e., signal) on its three semaphores. All semaphores are binary semaphores initialized to one. Which one of the following represents a deadlock-free order of invoking the P operations by the processes?

A shared variable x, initialized to zero, is operated on by four concurrent processes W, X, Y, Z as follows. Each of the processes W and X reads x from memory, increments by one, stores it to memory, and then terminates. Each of the processes Y and Z reads x from memory, decrements by two, stores it to memory, and then terminates. Each process before reading x invokes the P operation (i.e., wait) on a counting semaphore S and invokes the V operation (i.e., signal) on the semaphore S after storing x to memory. Semaphore S is initialized to two. What is the maximum possible value of x after all processes complete execution?

A certain computation generates two arrays a and b such that a[i]=f(i) for 0 ≤ i < n and b[i]=g(a[i]) for 0 ≤ i < n. Suppose this computation is decomposed into two concurrent processes X and Y such that X computes the array a and Y computes the array b. The processes employ two binary semaphores R and S, both initialized to zero. The array a is shared by the two processes. The structures of the processes are shown below.

Process X:                         Process Y:
private i;                         private i;
for (i=0; i < n; i++) {            for (i=0; i < n; i++) {
   a[i] = f(i);                       EntryY(R, S);
   ExitX(R, S);                       b[i]=g(a[i]);
}                                 }

Which one of the following represents the CORRECT implementations of ExitX and EntryY?

(A)

ExitX(R, S) {
  P(R);
  V(S);
}

EntryY (R, S) {
  P(S);
  V(R);
}

(B)

ExitX(R, S) {
  V(R);
  V(S);
}

EntryY(R, S) {
  P(R);
  P(S);
}

(C)

ExitX(R, S) {
  P(S);
  V(R);
}
EntryY(R, S) {
  V(S);
  P(R);
}

(D)

ExitX(R, S) {
  V(R);
  P(S);
}
EntryY(R, S) {
  V(S);
  P(R);
}

A process executes the code

fork();
fork();
fork(); 

The total number of child processes created is

Fetch_And_Add(X,i) is an atomic Read-Modify-Write instruction that reads the value of memory location X, increments it by the value i, and returns the old value of X. It is used in the pseudocode shown below to implement a busy-wait lock. L is an unsigned integer shared variable initialized to 0. The value of 0 corresponds to lock being available, while any non-zero value corresponds to the lock being not available.

  AcquireLock(L){
         while (Fetch_And_Add(L,1))
               L = 1;
   }
  ReleaseLock(L){
         L = 0;
   }

This implementation