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On Properties of the Inverse Method : Commutation of Instanciation and Full Covering of the Behavioral Cartography

When one performs an Inverse Method [5] on a Parametric Timed Automata [1] over an instance π0, one can instantiate some parameters at the very beginning of the analysis or at the end, with a restriction of the constraint K0 obtained in order to get a constraint over a subset of the parameters. In this report, we show that the results of either methods are the same. We present a theoretical proof and then an illustration of this property on the flip-flop example and the Root Contention protocol. We also present some results about the coverage of behavioral cartography and an illustration of the full covering on the SPSMALL memory.