vault backup: 2025-04-15 08:25:18

.obsidian/workspace.json

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Concurrent Systems/notes/13 -.md

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+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:
+$$S_{}^{(2)} \triangleq p \cdot S_{1}^{(2)}$$
+$$S_{1}^{(2)} \triangleq p \cdot S_{1}^{(2)}+v\cdot S^{(2)}$$
+$$S_{2}^{(2)} \triangleq v \cdot S_{1}^{(2)}$$