Temporal Abstract Domains

The specifications of the control units driving embedded systems often involve temporal properties. We aim at certifying them statically using the Abstract Interpretation framework and introduce several Abstract Domains dedicated to proving such temporal properties. This work defines the specificity of such domains, that we call Temporal Abstract Domains. We introduce a continuous-time abstraction, since this abstract and continuous representation of the time allows a fast computation of abstract invariants that are furthermore more precise than with discrete time. This also enables the definition of a canonical reduced-product between the domains. We finally present new abstract domain transformers that build more precise new domains with a reasonable additional cost with respect to the initial domain. An example of such a generic transformer introduces temporally-local disjunctions and is thus specific to temporal abstract domains.