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Consider two processes A and B both needing an instance of X. Assume priority of A is greater than B. Initially X will be assigned to A due to higher priority of A. But if before X completes execution, priority of B becomes greater than A, A can be put on hold and B can start execution. Now, during execution of B, if priority of A becomes greater, the same cycle continues- two processes trying to make progress but not able to do- livelock.
ref@ https://en.wikipedia.org/wiki/Deadlock#Livelock

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I think, as I remember there is low priority process which executing is in critical section and at the same point of time a high priority job comes in ready queue. because of M.E that process can not go into CS so though process high priority but it has to wait unitl Low priority process completes its execution

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Prateek Dwivedi asked Jun 27, 2015
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This is a question from Operating System concepts by Silberschatz, Gagne and Galvin. On very first go I could make that in such a situation deadlock can never occur. But ...