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# GATE | GATE-CS-2006 | Question 85

Consider the following snapshot of a system running n processes. Process i is holding Xi instances of a resource R, 1 <= i <= n. currently, all instances of R are occupied. Further, for all i, process i has placed a request for an additional Yi instances while holding the Xi instances it already has. There are exactly two processes p and q such that Yp = Yq = 0. Which one of the following can serve as a necessary condition to guarantee that the system is not approaching a deadlock?
(A) min (Xp, Xq) < max (Yk) where k != p and k != q
(B) Xp + Xq >= min (Yk) where k != p and k != q
(C) max (Xp, Xq) > 1
(D) min (Xp, Xq) > 1

Explanation:

Deadlock refers to a specific condition when two or more processes are each waiting for another to release a resource, or more than two processes are waiting for resources.

Solution:

Necessary condition to guarantee no deadlock which means without satisfying this condition, no deadlock is possible. Both the process p and q have no additional requirement; they both can be finished releasing Xp + Xq resources without asking for any additional resource.
Using this, we can finish one more process only if condition B is satisfied. If the resources released by p and q are sufficient for another process waiting for Yk resources, then system is not approaching deadlock.
i.e Xp+Xq > min (Yk) where k != p and k != q

Note: Option B just ensured that the system can proceed from the current state. It does not guarantee that there wonâ€™t be a deadlock before all processes are finished.

This solution is contributed by Nitika Bansal

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