Issue No. 04 - April (1997 vol. 46)

ISSN: 0018-9340

pp: 491-494

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.588065

ABSTRACT

<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>

INDEX TERMS

Decision diagrams, BDD, symmetric functions, multiple-valued functions, complexity, asymptotic approximation, average case.

CITATION

T. Sasao, R. J. Barton III, D. S. Herscovici and J. T. Butler, "Average and Worst Case Number of Nodes in Decision Diagrams of Symmetric Multiple-Valued Functions," in

*IEEE Transactions on Computers*, vol. 46, no. , pp. 491-494, 1997.

doi:10.1109/12.588065

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