In deadlock avoidance, what is a safe state and how is the notion of safety used to decide whether to grant a resource request?

Introduction / Context:
Deadlock avoidance strategies, such as Bankers algorithm, use the concept of a safe state to decide whether a new resource request can be granted without risking deadlock. Instead of waiting for deadlocks to occur, the system proactively checks whether it can still schedule all processes to completion. This question asks you to define a safe state and explain how it is used in deadlock avoidance.

Given Data / Assumptions:

• Processes declare their maximum resource needs in advance.
• The system tracks current allocation and remaining needs.
• Deadlock avoidance algorithms simulate granting a request and test for safety.
• A safe state implies the existence of at least one completion sequence.

Concept / Approach:
A safe state is one where the operating system can find an ordering of processes such that each process in turn can obtain the resources it still needs, run to completion and release its resources, allowing the next process in the sequence to continue. If such a sequence exists, the system is safe because it can avoid deadlock even if all processes demand their maximum resources. In avoidance algorithms, the system considers a tentative grant of a new request, then checks whether the resulting state is safe. Only if safety is preserved will the request actually be granted.

Step-by-Step Solution:
Step 1: Recall that safety does not mean that a particular schedule is fixed, only that at least one safe sequence exists. Step 2: Understand that in a safe sequence, each process can be given enough resources to finish, one after another, without deadlock. Step 3: Recognise that Bankers algorithm simulates resource allocation to test whether a safe sequence still exists after a tentative grant. Step 4: Note that if no such sequence can be found, the state is considered unsafe and the request is denied or delayed. Step 5: Choose the option that defines a safe state in terms of a completion sequence and links safety to the decision to grant requests.

Verification / Alternative check:
Deadlock avoidance theory formally defines a safe state as one from which the system can allocate resources to each process up to its maximum in some order and still avoid deadlock. Textbooks explicitly connect this definition to the procedure used in Bankers algorithm: simulate allocation, test safety, then commit or roll back. This matches the wording of the correct option and not the other options that describe termination or idle resources.

Why Other Options Are Wrong:
Option B describes a drastic step of terminating all processes, which is not the definition of a safe state. Option C refers to a state where resources are idle and no processes run, which may be safe but does not capture the general idea of safety for arbitrary workloads. Option D mentions a state where a deadlock already exists, which contradicts the idea of safety, since safe states by definition avoid deadlock.

Common Pitfalls:
A common confusion is to think that an unsafe state means that deadlock has already occurred. In fact, unsafe means only that the system cannot guarantee avoidance, not that deadlock is present. Another pitfall is to assume that there must be a unique safe sequence; in reality, many different safe sequences may exist, and finding one is enough to classify the state as safe.

Final Answer:
A safe state is one in which there exists some sequence of process execution that lets every process obtain needed resources and complete without deadlock, and deadlock avoidance algorithms grant new requests only if the resulting state remains safe.