Eecient Variable Ordering and Partial Representation Algorithms

In this paper we introduce some new methods for constructing Ordered Partial Decision Diagrams (OPDDs). The algorithms are eeective in capturing a signiicant fraction of a given function's truth table using only a very small space. Using such data structures the importance of a variable in a Boolean function can be computed. Such methods can easily be used for computing variable orders to construct BDDs. The measures of a variable's importance are based on information-theoretic criteria, and require computation of the en-tropy of a variable for a given function. We have found that entropy measures can be quite eeective in distinguishing the importance of variables. The results show a very encouraging approach towards the solution of this well known problem.

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