Generalizing Simulation to Abstract Domains

We introduce a notion of subsumption for domains used in abstract interpretation. We show that subsumption has the same properties and applications in the context of abstract interpretation that simulation has for transition systems. These include a modal characterisation theorem, a fixed point characterisation, and the construction of property-preserving abstractions. We use the notion of conjugate functions from algebraic logic to develop bisubsumption, an order-theoretic generalisation of bisimulation to Boolean domains. We prove a representation theorem that relates simulation and subsumption.

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