Critical section correctness: to prevent race conditions, how many processes may be inside their critical section at the same time?

Introduction / Context:
Race conditions occur when multiple processes or threads access shared data concurrently and the final outcome depends on unpredictable interleavings. The critical section problem asks for a mechanism to ensure mutual exclusion so that shared state remains consistent. The fundamental safety requirement is that at most one process is executing the critical section at any instant.

Given Data / Assumptions:

• We consider a shared resource protected by a critical section protocol.
• We want to avoid races and ensure correct behavior.
• We are not considering liveness or fairness constraints in the answer, only safety.

Concept / Approach:

Mutual exclusion guarantees that only one process may enter the critical section at a time. This can be implemented with locks, semaphores, monitors, atomic instructions, or transactional memory. If two or more processes are allowed inside simultaneously, shared invariants can be violated, causing data corruption or inconsistent results. Therefore, the safe limit is a single process at any moment.

Step-by-Step Solution:

Verification / Alternative check:

Classical solutions (Peterson algorithm, bakery algorithm) and modern primitives all enforce the invariant that only one thread holds the lock at a time, preserving shared state consistency.

Why Other Options Are Wrong:

• 0: would deadlock progress; no one could enter to perform work.
• 8 or 16: allowing multiple concurrent entrants breaks mutual exclusion unless the resource supports safe concurrent access, which contradicts the critical section definition.
• None of the above: incorrect because exactly one is correct.

Common Pitfalls:

• Confusing reader writer locks where multiple readers may enter with general critical sections that protect write access.

Final Answer:

1.