In this paper a systematic method for generating, comparing and proving the properties of transition systems is presented. It is assumed that any property of a system can be defined by giving a set of ‘target’ states and a type of reachability. Ten different types of reachability are proposed; by appropriately choosing the set of target states, a family of ten potentially different properties is generated. The main conclusion is that the reachability types and therefore the system properties, can be characterized by simple relations involving the set of the possible initial states and fixed points of certain continuous predicate trasformers depending on the set of target states. As a consequence, in order to prove a given property it is sufficient to compute iteratively greatest or least fixed points of continuous predicate transformers.
Some examples are presented which show how the results can be applied to prove the properties of concurrent systems represented by non-deterministic models.
