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