Consider three processes P1, P2, and P3 running identical code, as shown in the pseudocode below. A and B are two binary semaphores initialized to 1 and 0 , respectively. $X$ is a shared variable initialized to 0 . Each line in the pseudocode is executed atomically. Pseudocode of P1, P2, and P3

Wait(A);

Print(*);

X = X+1;

If (X == 2)

    {

        Print($);

        Signal(B);

    }

Signal(A);

Wait(B);

Print(#);

Signal(B);

Assume that any of the three processes can start to execute first and context switching can happen between these processes at any arbitrary time and in any arbitrary order. Which of the following patterns is/are possible to be generated as an outcome of the execution of these three processes?

Consider the following two threads T1 and T2 that update two shared variables a and b. Assume that initially $a = 1$ and $b = 1$. Though context switching between threads can happen at any time, each statement of T1 or T2 is executed atomically without interruption.

T1:
$a = a + 1$;
$b = b + 1$;

T2:
$b = 2 * b$;
$a = 2 * a$;

Which one of the following options lists all the possible combinations of values of a and b after both T1 and T2 finish execution?

Consider the following code snippet using the fork() and wait() system calls. Assume that the code compiles and runs correctly, and that the system calls run successfully without any errors.

int x = 3;
while(x > 0) {
  fork();
  printf("hello");
  wait(NULL);
  x--;
}

The total number of times the printf statement is executed is _______

Consider the two functions incr and decr shown below.

incr() {
  wait(s);
  X = X+1;
  signal(s);
}

decr() {
   wait(s);
   X = X-1;
   signal(s);
}

There are 5 threads each invoking incr once, and 3 threads each invoking decr once, on the same shared variable X. The initial value of X is 10.

Suppose there are two implementations of the semaphore s, as follows:

I-1: s is a binary semaphore initialized to 1.

I-2: s is a counting semaphore initialized to 2.

Let V1, V2 be the values of X at the end of execution of all the threads with implementations I-1, I-2, respectively.

Which one of the following choices corresponds to the minimum possible values of V1, V2, respectively?