GATE - 2008 | OS | The P and V operations on counting semaphores, where s is a counting

GATE - 2008 [Operating System]

Question:

The P and V operations on counting semaphores, where s is a counting semaphore, are defined as follows:

P(s) : s =  s - 1;
  if (s  < 0) then wait;
V(s) : s = s + 1;
  if (s <= 0) then wakeup a process waiting on s;

Assume that Pb and Vb the wait and signal operations on binary semaphores are provided. Two binary semaphores Xb and Yb are used to implement the semaphore operations P(s) and V(s) as follows:

P(s) : Pb(Xb);
  s = s - 1;
  if (s < 0) {
   Vb(Xb) ;
   Pb(Yb) ;
  }
  else Vb(Xb); 

V(s) : Pb(Xb) ;
  s = s + 1;
  if (s <= 0) Vb(Yb) ;
  Vb(Xb) ;

The initial values of Xb and Yb are respectively

A	0 and 0
B	0 and 1
C	1 and 0
D	1 and 1

     

Solution:

Option (C) is Correct.

x_b must be 1 because both P(s) operation and V(s) operation perform P_b(x_b) first.

So if x_b=0, then all the process performing these operations will be blocked.

Y_b must be '0' initially, because if Y_b is '1' initially then two process can be in critical section at the same time.

So answer is Option (C).

Thank You