Deductive Verification of Modular Systems
COMPOS'97 Revised Lectures from the International Symposium on Compositionality: The Significant Difference
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This thesis presents a compositional methodology for the verification of reactive and real-time systems. The correctness of a given system is established from the correctness of the system''s components, each of which may be treated as a system itself and further reduced. When no further reduction is possible or desirable, global techniques for verification may be used to verify the bottom-level components. Transition modules are introduced as a suitable compositional model of computation. Various composition operations are defined on transition modules, including parallel composition, sequential composition, and iteration. A restricted assumption-guarantee style of specification is advocated, wherein the environment assumption is stated as a restriction on the environment''s next-state relation. Compositional proof rules are provided in accordance with the safety-progress hierarchy of temporal properties. The compositional framework is then extended naturally to real-time transition modules and discrete-time metric temporal logic.