This paper formalizes an incremental approach to design flow-control oriented hardware devices described by Moore machines. The method is based on successive additions of new behaviors to a simple device in order to build a more complex one. The new behaviors added must not override the previous ones. A set of CTL formulae is assigned to each step of the design. The links between the formulae of two consecutive design steps are formalized as a set of formula-transformations F , stating that : a

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... CTL formula f is satisfied on a design at step i, iff F (f ) is satisfied on the design extended at step i+1. This result has been applied during the design of bus protocol converters in the context on non-regression analysis. It could also be applied in order to simplify both system and formulae in particular cases.