Abstraction and Refinement in Configuration Structures

An abstraction operator for configuration structures is defined and it is proven that it is left inverse to the traditional refinement operator. The abstraction operator describes how concrete behaviour looks when observed from a more abstract level, where the difference between concrete and abstract is given by a transformation mapping. This generates a notion of implementation: L is said to implement H iff L is mapped to H by the abstraction operator. The implementation relation generated by the abstraction operator is strictly more general than the implementation function defined by a refinement operator, thus allowing a more flexible design process for distributed systems.