Binary Decision Diagrams: A Mathematical Model for the Path-Related Objective Functions
نویسندگان
چکیده
This paper describes a mathematical model for all path length parameters (APL: Average Path Length, LPL: Longest Path Length, and SPL: Shortest Path Length) of Binary Decision Diagrams (BDDs). The proposed model is based on an empirical analysis of randomly generated Boolean functions. The formal core of the developed model is a unique equation for the path-related objective functions over the set of BDDs derived from Boolean functions with given number of variables and Sum of Products (SOP) terms. Simulation results show good correlation between the theoretical results and those predicted by the mathematical model. This model provides an estimation of the performance of a circuit prior to its final implementation, and can be applied to Boolean functions with any number of variables, any number of product terms, and any variable ordering method. Key-Words: Evaluation time estimation, Binary Decision Diagram (BDD), Path Length of BDDs, Boolean functions
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