Binary Relations for Abstraction andRe
نویسنده
چکیده
By employing Kripke structures as a common framework for system speciications, implementations, and abstractions, we study the standard means for relating a spec-iication to its reenement 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 speciications, implementations, and abstractions possess logical properties as well, we study sound subsets of temporal logic (more speciically, modal mu-calculus) that can be used for stating necessarily-true propositions and possibly-true propositions about speciications and abstractions. By extending Kripke structures to modal-transition systems, we are able to employ full modal mu-calculus as a sound logic for necessarily-and 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 reenement and abstraction.
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