Generalised Reactive Processes Sample Clauses

Generalised Reactive Processes. Our approach to hybrid semantics is to generalise the theory of reactive designs to ac- commodate continuous time trajectories. In our new model, continuous variables are effectively embedded into the standard relational calculus through a generalised notion of trace, rather than added as a new core concept, which greatly simplifies reasoning. We first make the observation that traces need not be given a concrete model, as they are in the UTP book [30], but can be characterised algebraically. We introduce the following �� abstract operators: , which denotes the empty trace,x � y, which denotes trace con- − ≤ catenation,x y, a partial order on traces which denotes thatxis a prefix ofy, and finallyx ywhich, when possible, removes the prefixyfromx. The behaviour of these functions is characterised by the following axioms:

Generalised Reactive Processes. ‌ In the section we construct a UTP theory which generalises the standard UTP theory of reactive processes [29, 9] with an abstract model of trace. In the UTP model, the trace can only be a discrete sequence of events, as used by process algebras like CSP. However, for hybrid computation we of course require continuously evolving variables, rather than simply discrete snapshots at given intervals. Therefore, we generalise the trace model such that constructions like piecewise continuous functions can also be supported. This thus provides an important first towards the hybrid relational calculus. Parts of this section have been submitted as a paper to Information Processing Letters [18].