An n-ary semaphore S(n)(p,v) is a process used to ensure that there are no more than n istances of the same activity concurrently in execution. An activity is started by action p and is terminated by action v.

The specification of a unary semaphore is the following:
$$S^{(1)} \triangleq p \cdot S_{1}^{(1)}$$
$$S_{1}^{(1)} \triangleq p \cdot S_{1}^{(1)}$$
The specification of a binary semaphore is the following:
$$S_{}^{(2)} \triangleq p \cdot S_{1}^{(2)}$$
$$S_{1}^{(2)} \triangleq p \cdot S_{1}^{(2)}+v\cdot S^{(2)}$$
$$S_{2}^{(2)} \triangleq v \cdot S_{1}^{(2)}$$