Another Glance at the Alpern-Schneider Characterization of Safety and Liveness in Concurrent Executions

In order to derive a result such as the Alpern Schneider theorem char acterizing safety and liveness properties of concurrent program executions it is shown that all that is needed is a preserving map between com plete Boolean algebras Every property becomes a conjunction of a safety and a liveness property and safety properties can be characterized by sets of con gurations that are to be avoided Aside from the original result of B Alpern and F B Schneider we also provide a new application by considering transition systems with a UNITY style logic Safety properties are characterized by a set of forbid den pairs of successive states and progress properties are those allowing all possible state successor pairs Every property of a transition system is shown to be a conjunction of a safety and a progress property