GATE CS 2013 Q39 — Concurrency and Synchronization

A certain computation generates two arrays a and b such that $a[i] = f(i)$ for $0 \leq i < n$ and $b[i] = g(a[i])$ for $0 \leq i < n$. 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:

private i; 
for (i=0; i< n; i++) { 
 a[i] = f(i); 
 ExitX(R, S); 
} 

Process Y:

private i;
for (i=0; i< n; i++) { 
  EntryY(R, S); 
  b[i] = g(a[i]); 
}

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