Reasoning about Conditional Progress Properties

In some otherwise attractive formalisms, it can be diicult or even impossible to specify progress in such a way that a component of a distributed system can be proved correct independent of its environment. This problem arises because the nested dependencies between the component and its environment cannot be conveniently expressed in the formalism. A typical example is a communication protocol, which is supposed to provide reliable data transfer even over channels that are unboundedly lossy: the channels only deliver messages if the protocol transmits them often enough, while the protocol only guarantees reliable service if the channels deliver suuciently many messages. This paper investigates the extent to which such progress speciications can be dealt with using predicate calculus and a single temporal operator (leads-to) having a simple proof theory. It turns out that under the proper semantic interpretation, many progress speciications expressing complex dependences can be represented using certain boolean combinations of leads-to properties. By adding two simple inference rules to an existing proof theory, we obtain a (relatively) complete theory for a large class of conditional progress properties, without the complexity of the full temporal logic; such a theory can be used with various compositional speciication formalisms. Based on the results, an approach to speciication of protocol progress is outlined and illustrated with an example.