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Average and worst case number of nodes in decision diagrams of symmetric multiple-valued functions

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4 Author(s)
Butler, J.T. ; Dept. of Electr. & Comput. Eng., Naval Postgraduate Sch., Monterey, CA, USA ; Herscovici, D.S. ; Sasao, T. ; Barton, R.J., III

We derive the average and worst case number of nodes in decision diagrams of r-valued symmetric functions of n variables. We show that, for large n, both numbers approach nr/rl. For binary decision diagrams (r=2), we compute the distribution of the number of functions on n variables with a specified number of nodes. Subclasses of symmetric functions appear as features in this distribution. For example, voting functions are noted as having an average of n2/6 nodes, for large n, compared to n2/2, for general binary symmetric functions

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Computers, IEEE Transactions on  (Volume:46 ,  Issue: 4 )