Contexts, refinement and determinism

Abstract

In this paper we have been influenced by those who take an "engineering view" of the problem of designing systems, i.e. a view that is motivated by what someone designing a real system will be concerned with, and what questions will arise as they work on their design. Specifically, we have borrowed from the testing work of Hennessy, De Nicola and van Glabbeek, e.g. [13, 5, 21, 40, 39]. Here we concentrate on one fundamental part of the engineering view and where consideration of it leads. The aspects we are concerned with are computational entities in contexts, observed by users. This leads to formalising design steps that are often left informal, and that in turn gives insights into non-determinism and ultimately leads to being able to use refinement in situations where existing techniques fail.

Refinement for Probabilistic Systems with Nondeterminism

“…So, our specification language would need to allow us to make this distinction and, most helpfully, only allow probabilistic choice to be specified in situations where it makes sense, as in the case of specifying the robot. We have done previous work on adding causality (back) into process algebras, and the work presented here forms the basis for a probabilistic causal process algebra (CPA) [12], or for a probabilistic language for interactive branching processes (IBPs) [10] which we have also talked about before, which forms the subject of another paper yet to be published.…”

“…The pair of mappings ( FA PPFA , vA FA PPFA ) define a vertical refinement ⊑ FA PPFA as they are a Galois connection [10]. This is the content of Theorem 7, but first some preliminary results.…”

“…We go no further with this point in this paper, but note that, in the non-probabilistic setting, we have considered this previously in[10].…”