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ROBDD Optimization Using Sub Graph Complexity


Mohamed Raseen, K.Thanushkodi


Vol. 8  No. 8  pp. 137-145


This paper describes a novel method of variable reordering for Reduced Ordered Binary Decision Diagrams (ROBDD). The proposed method results in ROBDD with lesser number of nodes and lesser APL. The variable order in ROBDD is important since it affects the number of ROBDD nodes. The problem of constructing an ROBDD with minimum number of nodes has become of growing importance since there is no unique method that can be used to obtain the least number of nodes for all Boolean functions. In this work, the proposed variable ordering methods uses the graph topology to find the optimal variable ordering; therefore the input Boolean function (benchmark circuits) are converted to a unidirectional graph. The variable order is found by substituting the values of logic 1 and logic 0 for all the variables. The variable that produces minimal sub graph is assigned as next variable in variable order. This process of assignment and selection is repeated iteratively until all variables are selected. The efficiency of the proposed method is demonstrated by building the ROBDD for selected benchmark circuits. The number of nodes is then compared for proposed method with existing methods in Colorado University Decision Diagram (CUDD) package. The experimental results using benchmark circuits show that the proposed method is an encouraging approach towards minimizing the evaluation time and number of nodes for a Boolean function.


Binary Decision Diagrams, Variable Ordering, Graph Representations, Boolean Functions Representations