CEG 7370: Distributed Computing Principles

Semantics of Semaphores

1. Semaphore Definition

   P(s) ≡ ‹ await s > 0 → s := s-1 ›
   V(s) ≡ ‹ s := s+1 ›

2. Semaphore Invariant

   nP ≤ nV + initValue
   s = initValue + nV - nP
   SEM: s ≥ 0
   

3. Synchronization Rule

   {R and B} S {Q} {R} ‹await B → S › {Q}

4. Semaphore Ops

   (R and s > 0) ⇒ Qss-1 {R} P(s) {Q}

   R ⇒ Qss+1 {R} V(s) {Q}