The safety and liveness properties of the network protocol based on TLA

We propose a definition of the class of all fairness properties of concurrent systems. In this work, we introduce to the fair transition system, and then discuss the relation among safety property, liveness property and fairness property in the temporal logic of actions. On the way, we give a recent overview work on fairness in reactive and concurrent systems, and innovatively prove the relation among of the fairness. Furthermore, we consider a ring-based leader election protocol. Leader election is an important protocol in distributed computing. We have proven or verified that this protocol satisfies safety and liveness properties, and use the temporal logic of actions for formalization and specification.