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Shared multiple-valued decision diagrams for multiple-output functions

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2 Author(s)
H. M. H. Babu ; Dept. of Comput. Sci. & Electron., Kyushu Inst. of Technol., Iizuka, Japan ; T. Sasao

In this paper, we propose a method to represent multiple-output functions using shared multiple-valued decision diagrams (SMDDs). We show an algorithm for pairing the input variables of binary decision diagrams (BDDs). We also present the pair sifting that moves pairs of 4-valued input variables to speed up the normal sifting, and to produce compact SMDDs. The size of the SMDD is the total number of non-terminal nodes excluding the nodes for output selection variables. We derive the sizes of SMDDs for general functions and symmetric functions. From experimental results, we conjecture that, for n>1, the sizes of SMDDs for bit-counting functions (wgt n) and incrementing functions (inc n) are n[log2n]+n-2([log2n]) and 2n-1, respectively, where n is the number of binary input variables, and [a] denotes the largest integer not greater than a. We also compare our method with other one. Experimental results show the efficiency of our method

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Multiple-Valued Logic, 1999. Proceedings. 1999 29th IEEE International Symposium on

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