Binary Relations for Abstraction and Re nement

By employing Kripke structures as a common framework for system speci cations, implementations, and abstractions, we study the standard means for relating a speci cation to its re nement and for relating an implementatation to its abstraction. The classic tools of homomorphism and Galois connection are dissasembled and characterized in terms of binary simulation relations that possess desirable structural properties. Because speci cations, implementations, and abstractions possess logical properties as well, we study sound subsets of temporal logic (more speci cally, modal mucalculus) that can be used for stating necessarily-true propositions and possibly-true propositions about speci cations and abstractions. By extending Kripke structures to modal-transition systems, we are able to employ full modal mu-calculus as a sound logic for necessarilyand possibly-true propositions, and we can characterize a modal-transition system by the logical propositions that hold true for it. Most of the paper's technical development is scattered throughout the research literature, and the paper's main contribution is assembling the technical material into a coherent, useful methodology for system re nement and abstraction.