Transformations preserving properties and properties preserved by transformations in fair transition systems (extended abstract)

Abstract

Chandy and Misra's Unity, Back's Action Systems and Lamport's Temporal Logic of Actions (TLA) are three prime examples of specification formalisms for concurrent systems viewed as fair transition systems. The first two examples, and to a lesser extent the latter, also advocate a design methodology for formal derivation of concurrent systems or, rather, concurrent algorithms. Their program can be summarized as positing that algorithms should be designed without specific program control being forced upon the designer and that algorithms should be specified using properties that are (easily shown to be) preserved by the various transformations that one might use during the derivation process. For Misra and Chandy such transformations include union (i.e., parallel composition) and some forms of refinement but not hiding of variables. Back does consider hiding but ignores union as a property preserving transformation; as does, e.g., Lamport in his TLA.

The first aim of our research is to further this program and to find properties and a larger class of transformations (including all of the above mentioned) such that the properties are preserved by this class. A typical result is that the Unity unless property, that is known to be preserved by union and superposition, is also preserved by hiding and refinement (as we define them).

Our second aim, prompted by the growth of the collection of transformations and novel to this approach, is to consider their interaction—e.g., a superposition should refine the underlying program.

Our third, also novel, aim is to investigate how much ‘leeway’ there is in defining such properties and transformations. Here, one result is that the Unity invariance property, p iv in T, is the weakest property that implies that p is true everywhere on the computations of T and that is preserved by union.

This abstract's results are summarized in Table 2 and should be contrasted with Table 1 which summarizes the relevant ‘state of the art’.

We use temporal logic and a subset of it YAL as program notation. Our results, however, are in no way restricted to YAL and apply equally well to, e.g., TLA, Unity, Action Systems, Manna and Pnueli's transition systems or Lynch and Tuttle's I/O automata.

Supported by the Deutsche Forschungsgemeinschaft, SFB 124, TP C1

Currently working in ESPRIT project P6021: “Building Correct Reactive Systems (REACT)”.