The task of guaranteeing that only one of several processes enters the same critical section. Forgetting mutual exclusion may lead to race conditions, which are difficult to find bugs. There are several methods to achieve mutual exclusion:

Mutex variable:
One (or several) variables which are counted up/down or are changed by some specific algorithm (e.g. Bakery algorithm) to reach mutual exclusion. With the current hardware support of atomic test&set operations these are easy to implement.
A counter set to a starting number, which can be hold by exactly that number of processes. More processes can only get hold of the semaphore if earlier processes given it up. Internally often uses a mutex variable.
A section of code (sometimes also an object), which by itself allows only one process to enter it. Within the monitor, processes can decide to wait for some conditions which allows another process to enter the monitor. Java's "synchronized" construct can be seen as a monitor.

Each method for mutual exclusion can be implemented using another one as basis.

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