Superposition refinement of reactive systems

Abstract

Superposition refinement enhances an algorithm by superposing one computation mechanism onto another mechanism, in a way that preserves the behavior of the original mechanism. Superposition seems to be particularly well suited to the development of parallel and distributed programs: an originally simple sequential algorithm can be extended with mechanisms that distribute control and state information to many processes, thus permitting efficient parallel execution of the algorithm. We will show in this paper how superposition of reactive systems is expressed in the refinement calculus. We illustrate the power of this method by a case study, showing how a distributed broadcasting system is derived through a sequence of superposition refinements.

Superposition: composition vs refinement of non-deterministic, action-based systems

“…In this paper, we have shown how the concept of superposition, as used in [6,8,5,13,3], can subsume both composition and refinement of action-based designs. By adopting a categorical formalisation of designs for the language CommUnity, it becomes clear that composition and refinement are two ways of constructing complex designs from simpler ones that that are different because they are required to preserve different properties.…”

“…Superposition (or superimposition) has been proposed (and used) as a powerful mechanism for structuring the development of parallel programs and distributed systems [6,8,5,13,3]. It supports a layered approach to systems design by which we are allowed to build on (partially) developed components by augmenting them with new features while preserving the original properties.…”

Software Construction by Stepwise Feature Introduction

“…Superposition refinement can only add new attributes, it cannot remove old attributes. Superposition refinement (applied to reactive systems) is described in more detail in [8].…”

Retrenchment, Refinement, and Simulation

“…Likewise the device of introducing new operations at the concrete level which refine skip at the abstract level, is familiar from action refinement [10,11,12] -the actual presence or absence of dummy operations at the abstract level becomes then a matter of mere notation. Such operations also play a part in superposition refinement [13,14,15], where additional concrete computations are introduced to control the progress of a more abstract computation. Our introduction of the bandSelected variable and its influence on the abstract computation can be seen as being in the flavour of a superposition, though it cannot be a superposition in any strict sense since the abstract computation is interfered with at the more concrete level by the consequences of jamming.…”