GATE CS 2001 Q2.22 — Concurrency and Synchronization

In Peterson's algorithm for mutual exclusion between two processes $i$ and $j$:

• The boolean array flag represents the intent of each process to enter its critical section. Setting flag[i] = true means process $i$ wants to enter.
• The variable turn resolves conflicts when both processes try to enter simultaneously. By setting turn = j, process $i$ politely yields the turn to process $j$.

For process $i$ to safely enter its critical section, it must wait (busy-wait) if and only if:

1. The other process $j$ wants to enter the critical section: flag[j] == true.
2. It is currently process $j$'s turn to enter: turn == j.

Thus, the busy-waiting condition (predicate $P$) in the while loop of process $i$ must be:

$$\text{flag}[j] = \text{true} \text{ and } \text{turn} = j$$

If either of these conditions is false (e.g., if process $j$ is not interested, or if the turn has been given back to $i$), process $i$ breaks out of the loop and safely enters its critical section, ensuring mutual exclusion.

Therefore, the correct option is B.