An efficient estimation of the ROBDD's complexity

This paper describes a new mathematical model for the estimation of reduced ordered binary decision diagram's (ROBDD's) complexity, for any Boolean function with different degrees of variables complexity. The model is capable of predicting the maximum possible ROBDD complexity for Boolean functions with given number of variables. The proposed model is also capable of predicting the number of product terms in the Boolean function that will correspond to the maximum complexity of the ROBDD. This mathematical model works for any type of variable reordering method, and will enable the system performance to be analyzed without building the ROBDD. Since ROBDD complexity can be predicted without building it, a great reduction in terms of time complexity for VLSI CAD designs can be achieved and very useful clues to tackle ROBDD optimization problems in the design of digital circuits can also be obtained.