GATE - 2013 | OS | A shared variable x, initialized to zero, is operated on by four concurrent

GATE - 2013 [Operating System]

Question:

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	-2
B	-1
C	1
D	2

    

Solution:

Option (D) is Correct.

Suppose, 'W' executes first, and makes the value of semaphore S=1.

Now it increments the value of x to 1 and comes out and makes S=2.

Now 'X' executes, where the value of x=1 is stored in R₁ and then R₁ is incremented and the value in R₁ is 2.

Now, 'X' gets preempted.

Also to be noted that the value of semaphore S is now '1' because the execution during process X got preempted and wasn't able to increase the value of S to 2.

Now, process Y will get completely executed and then Z will get completely executed.

Now the value of 'x' is -3.

Now again 'X' will get executed and the value stored in R₁ i.e., '2' will get stored in 'x'.

So the value in 'x' will be finally 2.

So the maximum possible value of 'x' is 2.

Thank You