GATEverse — GATE CSE previous year questions

Consider the following snapshot of a system running $n$ concurrent processes. Process $i$ is holding $X_i$ instances of a resource $R$ , $1 \leq i \leq n$ . Assume that all instances of $R$ are currently in use. Further, for all $i$ , process $i$ can place a request for at most $Y_i$ additional instances of $R$ while holding the $X_i$ instances it already has. Of the $n$ processes, there are exactly two processes $p$ and $q$ such that $Y_p = Y_q =0$ . Which one of the following conditions guarantees that no other process apart from $p$ and $q$ can complete execution?

(A)

$X_p + X_q < \text{Min} \{Y_k \mid 1 \leq k \leq n, k \neq p, k \neq q \}$

(B)

$X_p + X_q < \text{Max} \{Y_k \mid 1 \leq k \leq n, k \neq p, k \neq q \}$

(C)

$\text{Min}(X_p,X_q) \geq \text{Min} \{Y_k \mid 1 \leq k \leq n, k \neq p, k \neq q\}$

(D)

$\text{Min}(X_p,X_q) \leq \text{Max} \{Y_k \mid 1 \leq k \leq n, k \neq p, k \neq q\}$