Efficient variable ordering and partial representation algorithm

Abstract

In this paper we introduce some new methods for constructing Ordered Partial Decision Diagrams (0P.DDs). The algorithms are effective in capturing a signi$cant fraction of a given function's truth table using, only a very small space. Using such data structurcs the importance of a variable an a Boolean function can be computed. Such methods can easily be used for computing effective variable orders to construct IIDDs. The measures of a variable's importance are based on information-theoretic criteria, and require computation of the entropy of a variable for a given function. W e have found that entropy measures can be quite eJFicient in distinguishing the importance of variables, and at times provide ve y egective variable order. The results show an encouraging approach towards the understanding and the solution of this well known problem.

Linearization of multi-output logic functions by ordering of the autocorrelation values

“…Thereby, the complexity of the computation and [16, 12, 0, 0, 6, 6, 0, 2, 0, 0, 10, 10, 0, 0, 6, 6] 10 18 2 [16,12,10,10,6,6,6,6, 0, 0, 0, 0, 0, 0, 0, 2] 4 28 3 [16,12,10,10,6,6,6,6, 0, 0, 0, 0, 0, 0, 0, 2] 15 28 final [16,12,10,10,6,6,6,6, 2, 0, 0, 0, 0, 0, 0, 0] -30…”

“…In some cases, the dynamic approach may fail to find a better set of variables within a given time limitation. The analytic approach defines a new ordered set of variables by considering the Boolean function properties like the values of the Walsh coefficients [26], the autocorrelation values [14,17,23] or the ambiguity of the variables [12]. This paper deals with a static linearization based on ordering the autocorrelation values for functions of large number of input variable for which the known linearization procedures may become impractical due to their high computational complexity.…”