Simple Doubt in counting semaphore

Question

Consider a non-negative counting semaphore S. During an execution, 16P (wait) operations, and 4V (signal) operations are issued in some order. The largest initial value of S for which at least three up operations will remain blocked is ___________

 

Can someone explain me the solution

Comments

Your ans. is correct. But why did you took -3 in RHS instead of +3

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-3 indicating that 3 processes are in the block state.

For ex - Let's take the value of counting semaphore = 10. (10 processes can be in the critical section)

If we have 12  processes then the value of counting semaphore will 10 -12 = -2 ( that means two process is in the critical section ).

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question says 3 up operation remain blocked thats why -3 if it would have asked for 3 operation remain blocked then we would have used +3. @pavan shetty

Answer 1

Assume Semaphore value as S

so according to question S-16(down operation) + 4(up operation)  <=  -3(here  – sign denotes number of process waiting in ready queue)

thus  S<=9   hence largest value of S is 9.