A Tight Consistent Delay Model for Black Boxes

A Boolean network with unknown components can be modeled as an AIG with black boxes (bb-AIG). The delay of an AIG is measured in terms of its maximum level after it is balanced. We propose a delay model for a black box which is consistent in that if a bb-AIG is refined by replacing an internal black box with another bb-AIG, its delay cannot decrease. It is also tight in that there exists an AIG which can replace a black box resulting in a delay equal to the estimated one. We prove that the proposed black box delay estimation is consistent and tight.