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Average and Worst Case Number of Nodes in Decision Diagrams of Symmetric Multiple-Valued Functions

 
: Butler, J.T.; Herscovici, D.S.; Sasao, T.; Barton, R.J.

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IEEE transactions on computers 46 (1997), No.4, pp.491-494
ISSN: 0018-9340
English
Journal Article
Fraunhofer IGD ()
Asymptotic Approximation; Average-Case; BDD; complexity; Decision Diagrams; Multiple-Valued Functions; Symmetric Functions

Abstract
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 (n involution r/r!). 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 (n squared/6) nodes, for large n, compared to (N sqaured/2), for general binary symmetric functions.

: http://publica.fraunhofer.de/documents/PX-5534.html