GATE CSE 1997 | Question: 6.8

Question

Each Process $P_i, i = 1\ldots 9$ is coded as follows

repeat 
    P(mutex)
    {Critical section}
    V(mutex)
forever

The code for $P_{10}$ is identical except it uses V(mutex) in place of P(mutex). What is the largest number of processes that can be inside the critical section at any moment?

• A. $1$
• B. $2$
• C. $3$
• D. None

Comments

The difference is in "vice versa".

In this question(Gate question), P10 is like V(mutext) CS V(mutex) but in your question it is V(mutex) CS P(mutex).

If you try to check now, be it any sequence, you cannot fit more than 3 process when mutex=1.

---

If nothing is given. We have to consider it's a binary semaphore? Am I right?

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Even if it’s vice versa then also more than 3 processes can be in C.S. :

The code I’m using for mutex :

Struct BSemaphore
{
    enum value(0,1);
    Queue type L;
}
P(BSemaphore mutex)
{
  if(mutex.value == 1)
      mutex.value = 0;
  else
      put the process in mutex.L;
      sleep();
V(BSemaphore mutex)
{
  if(mutex.L is empty)
      mutex.value = 1;
  else
      Select a process from mutex.L;
      wakeup();
    }
}

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Sequence :

mutex = 1;

p1 enters makes mutex = 0;

p10 enters makes mutex = 1;

p2 enters makes mutex = 0; // At this point there are 3 processes inside C.S.

p10 leaves , executes p(mutex) , but as it’s already zero goes to sleep and in queue.

p2 leaves executes v(mutex) , makes mutex = 1 and wakeup p10 . // At this point there is only 1 process inside C.S.

p3 enters makes mutex = 0;

p10 enters makes mutex = 1;

p4 enters makes mutex = 0 ; // At this point there are 4 processes inside C.S.

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And also answer of this should be 1 , due to two reasons :

1: Mutexes are not binary semaphore , mutex is a locking mechanism and the thread which acquired the lock can only release it.

2: Option d) says None , instead of none of the above.

Answer 1

is this correct?

Answer 2

option C

one process is executing critical section. all other are waiting. when P10 comes and increases semaphor value then the first process waiting in queue and P10 both comes into critical section. So there will be max 3 processes.

Comments

I think 3 will be the answer for the processes that can b in cs at same time but they r asking for processes at any moment of time plz crct me if I'm wrong