Consider the following snapshot of a system running 𝑛 concurrent processes.…

GATE Β· 2019 Β· CS Β· Computer Science & IT

Consider the following snapshot of a system running 𝑛 concurrent processes. Process 𝑖 is holding 𝑋𝑖 instances of a resource R, 1 ≀ 𝑖 ≀ 𝑛. Assume that all instances of R are currently in use. Further, for all 𝑖, process 𝑖 can place a request for at most π‘Œπ‘– additional instances of R while holding the 𝑋𝑖 instances it already has. Of the 𝑛 processes, there are exactly two processes 𝑝 and π‘ž such that π‘Œπ‘ = π‘Œπ‘ž = 0. Which one of the following conditions guarantees that no other process apart from 𝑝 and π‘ž can complete execution?

  1. A.

    Xp+Xq<Min{Yk∣1≀k≀n,kβ‰ p,kβ‰ q}X_p + X_q < \text{Min} \{Y_k \mid 1 \leq k \leq n, k \neq p, k \neq q \}

  2. B.

    Xp+Xq<Max{Yk∣1≀k≀n,kβ‰ p,kβ‰ q}X_p + X_q < \text{Max} \{Y_k \mid 1 \leq k \leq n, k \neq p, k \neq q \}

  3. C.

    Min(Xp,Xq)β‰₯Min{Yk∣1≀k≀n,kβ‰ p,kβ‰ q}\text{Min}(X_p,X_q) \geq \text{Min} \{Y_k \mid 1 \leq k \leq n, k \neq p, k \neq q\}

  4. D.

    Min(Xp,Xq)≀Max{Yk∣1≀k≀n,kβ‰ p,kβ‰ q}\text{Min}(X_p,X_q) \leq \text{Max} \{Y_k \mid 1 \leq k \leq n, k \neq p, k \neq q\}

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