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I get confused because i don't know if it is possible to use Test and Set primitives in case where more then one process can be enter in critical section at the same time.

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  • $\begingroup$ Test and Set is a primitive operation, used as a building block to implement more powerful operations. $\endgroup$
    – gnasher729
    Oct 29, 2017 at 7:42

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Your hunch is correct, they aren't equivalent. Test-and-set has a consensus number of 2, which means, roughly speaking, that it is only able to efficiently synchronize between 2 processes. See Why is the consensus number for test-and-set, 2?. Semaphores allow synchronization between an arbitrary number of processes (assuming no bound on the number of processes waiting on a semaphore).

It isn't really a “fair” comparison, since test-and-set is a hardware primitive while semaphores are a software interface. But if does show that test-and-set isn't sufficient to implement (wait-free) semaphores.

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