Computability structures, simulations and realizability

Abstract

We generalise the standard construction of realizability models (specifically, of categories of assemblies) to a wide class ofcomputability structures, which is broad enough to embrace models of computation such as labelled transition systems and process algebras. We consider a general notion ofsimulationbetween such computability structures, and show how these simulations correspond precisely to certain functors between the realizability models. Furthermore, we show that our class of computability structures has good closure properties – in particular, it is ‘cartesian closed’ in a slightly relaxed sense. Finally, we investigate some important subclasses of computability structures and of simulations between them. We suggest that our 2-category of computability structures and simulations may offer a useful framework for investigating questions of computational power, abstraction and simulability for a wide range of models.