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The existence of refinement mappingsby: M. Abadi, L. Lamport
Logic in Computer Science, 1988. LICS '88., Proceedings of the Third Annual Symposium on In Logic in Computer Science, 1988. LICS '88., Proceedings of the Third Annual Symposium on (1988), pp. 165-175.
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AbstractRefinement mappings are used to prove that a lower-level specification correctly implements a higher-level one. The authors consider specifications consisting of a state machine (which may be infinite-state) that specifies safety requirements and an arbitrary supplementary property that specifies liveness requirements. A refinement mapping from a lower-level specification S<sub>1</sub> to higher-level one <e1>S</e1><sub>2</sub> is a mapping from <e1>S</e1><sub>1</sub>'s state space to <e1>S</e1><sub>2</sub>'s state space that maps steps of S<sub>1</sub>'s state machine steps to steps of <e1>S</e1><sub>2</sub>'s state machine and maps behaviors allowed by S <sub>1</sub> to behaviors allowed by <e1>S</e1><sub>2</sub>. It is shown that under reasonable assumptions about the specifications, if <e1>S</e1><sub>1</sub> implements <e1>S</e1><sub>2</sub>, then by adding auxiliary variables to <e1>S</e1><sub>1</sub> one can guarantee the existence of a refinement mapping. This provides a completeness result for a practical hierarchical specification method
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