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Issue No.04 - April (1997 vol.46)
pp: 491-494
<p><b>Abstract</b>—We derive the average and worst case number of nodes in decision diagrams of <it>r</it>-valued symmetric functions of <it>n</it> variables. We show that, for large <it>n</it>, both numbers approach <tmath>${\textstyle{{{n^r} \over {r\,!}}}}.$</tmath> For binary decision diagrams (<it>r</it> = 2), we compute the distribution of the number of functions on <it>n</it> 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 <tmath>${\textstyle{n^2} \over 6}$</tmath> nodes, for large <it>n</it>, compared to <tmath>${\textstyle{{{n^2} \over 2}}},$</tmath> for general binary symmetric functions.</p>
Decision diagrams, BDD, symmetric functions, multiple-valued functions, complexity, asymptotic approximation, average case.
David S. Herscovici, Tsutomu Sasao, Jon T. Butler, "Average and Worst Case Number of Nodes in Decision Diagrams of Symmetric Multiple-Valued Functions", IEEE Transactions on Computers, vol.46, no. 4, pp. 491-494, April 1997, doi:10.1109/12.588065
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