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Average and Worst Case Number of Nodes in Decision Diagrams of Symmetric Multiple-Valued Functions
April 1997 (vol. 46 no. 4)
pp. 491-494
ASCII Text
x 
 
Jon T. Butler, David S. Herscovici, Tsutomu Sasao, Robert J. Barton III, "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.
 
 
BibTex
x
 
@article{ 10.1109/12.588065,
author = {Jon T. Butler and David S. Herscovici and Tsutomu Sasao and Robert J. Barton III},
title = {Average and Worst Case Number of Nodes in Decision Diagrams of Symmetric Multiple-Valued Functions},
journal ={IEEE Transactions on Computers},
volume = {46},
number = {4},
issn = {0018-9340},
year = {1997},
pages = {491-494},
doi = {http://doi.ieeecomputersociety.org/10.1109/12.588065},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Computers
TI - Average and Worst Case Number of Nodes in Decision Diagrams of Symmetric Multiple-Valued Functions
IS - 4
SN - 0018-9340
SP491
EP494
EPD - 491-494
A1 - Jon T. Butler,
A1 - David S. Herscovici,
A1 - Tsutomu Sasao,
A1 - Robert J. Barton III,
PY - 1997
KW - Decision diagrams
KW - BDD
KW - symmetric functions
KW - multiple-valued functions
KW - complexity
KW - asymptotic approximation
KW - average case.
VL - 46
JA - IEEE Transactions on Computers
ER -
 

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 ${\textstyle{{{n^r} \over {r\,!}}}}.$ 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 ${\textstyle{n^2} \over 6}$ nodes, for large n, compared to ${\textstyle{{{n^2} \over 2}}},$ for general binary symmetric functions.

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Index Terms:
Decision diagrams, BDD, symmetric functions, multiple-valued functions, complexity, asymptotic approximation, average case.
Citation:
Jon T. Butler, David S. Herscovici, Tsutomu Sasao, Robert J. Barton III, "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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