Question

Consider the following pseudocode, where S is a semaphore initialized to 5 in line#2 and counter is a shared variable initialized to 0 in line #1. Assume that the increment operation in line#7 is not atomic. 

1. int counter = 0; 
2. Semaphore S = init(5); 
3. void parop(void) 
4. { 
5.     wait(S); 
6.     wait(S); 
7.     counter++; 
8.     signal(S); 
9.     signal(S); 
10. } 

If five threads execute the function parop concurrently, which of the following program behavior(s) is/are possible?
 

• A. The value of counter is 5 after all the threads successfully complete the execution of \texttt{parop}.
• B. The value of counter is 1 after all the threads successfully complete the execution of \texttt{parop}.
• C. The value of counter is 0 after all the threads successfully complete the execution of \texttt{parop}.
• D. There is a deadlock involving all the threads.

Hint:

Counting semaphores limit concurrency but do not guarantee mutual exclusion unless carefully designed. Non-atomic operations inside critical sections can still cause race conditions.

Answer 1

The Correct Option is A, B, D

Step 1: Semaphore behavior analysis.
The semaphore \(S\) is initialized to 5. Each thread performs two \texttt{wait(S)} operations before entering the critical section. Hence, each thread requires 2 units of the semaphore to proceed.
With five threads, the total demand is \(5 \times 2 = 10\) units, but only 5 units are initially available. This immediately creates the possibility of blocking and deadlock.

Step 2: Possibility of deadlock (Option D).
A deadlock can occur if each of the five threads successfully executes the first \texttt{wait(S)} (reducing \(S\) from 5 to 0), and then all block at the second \texttt{wait(S)}. No thread reaches the \texttt{signal(S)} statements, so no semaphore units are released. Thus, a deadlock involving all threads is possible. Hence, (D) is correct.

Step 3: Effect of non-atomic increment.
The statement \texttt{counter++} is not atomic, meaning it consists of read, increment, and write steps. Even though semaphore control limits concurrency, it does not guarantee mutual exclusion for the increment operation. Hence, race conditions are possible.

Step 4: Analysis of Option (A).
In a favorable execution order where threads enter the critical section one at a time and no interleaving occurs during \texttt{counter++}, all five increments may be applied correctly. Thus, the final value of counter can be 5. Hence, (A) is possible.

Step 5: Analysis of Option (B).
Due to race conditions in the non-atomic increment, multiple threads may read the same value of counter and overwrite each other's updates. In an extreme case, all threads read 0 and finally write back 1. Therefore, the final value of counter can be 1. Hence, (B) is also possible.

Step 6: Analysis of Option (C).
If all threads successfully complete execution of \texttt{parop}, each must execute \texttt{counter++} at least once. Therefore, the value of counter cannot remain 0. Hence, (C) is not possible.

Step 7: Final conclusion.
The possible behaviors are (A), (B), and (D).