Binary decision diagrams with minimum expected path length.pdf

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Binary decision diagrams with minimum expected path length.pdf

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Binary decision diagrams with minimum expected path length

Binary Decision Diagram with Minimum Expected Path Length Yi-Yu Liu Kuo-Hua Wang TingTing Hwang C. L. Liu Department of Computer Science, National Tsing Hua University, Hsinchu 300, Taiwan Dept. of Computer Science and Information Engineering, Fu Jen Catholic University, Taipei, Taiwan Abstract We present methods to generate a Binary Decision Dia- gram (BDD) with minimum expected path length. A BDD is a generic data structure which is widely used in several fields. One important application is the representation of Boolean functions. A BDD representation enables us to evaluate a Boolean function: Simply traverse the BDD from the root node to the terminal node and retrieve the value in the terminal node. For a BDD with minimum expected path length will be also minimized the evaluation time for the corresponding Boolean function. Three efficient algorithms for constructing BDDs with minimum expected path length are proposed. 1. Introduction Binary Decision Diagram (BDD) was introduced in 1978 [1] as an effective way to represent Boolean functions that leads to efficient manipulation [2] and implementation [3]. Given a random input pattern, we can traverse the BDD to determine the outputing. There are previous works on mini- mizing the number of nodes in a BDD [4] [5] [6]. However, the number of nodes is not directly related to the evaluation time for a Boolean function. Rather, the evaluation time is directly related to the total expected path length of a BDD. In a logic circuit, the probabilities of occurance of the input variables are different. It follows that the evalua- tion time for different input combinations are also different. Consequently, a BDD with minimum expected path length will also have minimum evaluation time. To obtain a BDD with minimum expected path length, we need to develop (1) methods for computing the expected path length of a BDD (2) heuristics for ordering the variables in a BDD to mini- mize the expected path length. This paper is orga