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Consider a non-negative counting semaphore S. The operation P(S) decrements S, and V(S) increments S. During an execution, 20 P(S) operations and 12 V(S) operations are issued in some order. The largest initial value of S for which at least one P(S) operation will remain blocked is_______.

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Concepts:

V(S): Signal will increment the semaphore variable, that is, S++. 

P(S): Signal will decrement the semaphore variable., that is, S--. 

Data:

Initial counting semaphore = x

Signal operation = 12 V

Wait operation = 20 P

Since at least 1 process in blocked state

Final counting semaphore (F) = -1

Formula:

F ≥ x + 20P + 12V

Calculation:

-1 ≥ x + 20(-1) + 12(+1)

x ≤ 7

Therefore, largest value of initial semaphore count is 7

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