Specifying Computations Using Hyper Transition Systems

We study hyper transition systems as a formalism to give semantics to speciication languages which support both unbounded angelic and unbounded demonic non-determinism as well as recursion. Hy-per transition are a generalization of transition systems and are suited for the speciication of computations by means of properties that atomic steps in a computation have to satisfy. As an application we use a hy-per transition system to give an operational semantics to the language of Back's reenement calculus. This operational semantics abstracts from the internal conngurations and we prove it to be equivalent to the standard weakest precondition semantics. Finally, we propose a reenement relation that preserves the atomic step of a computation and generalizes the simulation relation on ordinary transition systems. This can be used to augment speciication languages with a form of concurrency.