Average path length of binary decision diagrams
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Authors
Sasao, Tsutomu
Matsuura, Munehiro
Butler, Jon T.
Subjects
Binary decision diagrams
BDD
average path length
APL
worst-case path length
BDD
average path length
APL
worst-case path length
Advisors
Date of Issue
2005-09
Date
September 2005
Publisher
Language
Abstract
The traditional problem in binary decision diagrams (BDDs) has been to minimize the number of nodes since this reduces
the memory needed to store the BDD. Recently, a new problem has emerged: minimizing the average path length (APL). APL is a
measure of the time needed to evaluate the function by applying a sequence of variable values. It is of special significance when BDDs
are used in simulation and design verification. A main result of this paper is that the APL for benchmark functions is typically much
smaller than for random functions. That is, for the set of all functions, we show that the average APL is close to the maximum path
length, whereas benchmark functions show a remarkably small APL. Surprisingly, however, typical functions do not achieve the
absolute maximum APL. We show that the parity functions are unique in having that distinction. We show that the APL of a BDD can
vary considerably with variable ordering. We derive the APL for various functions, including the AND, OR, threshold, Achilles’ heel, and
certain arithmetic functions. We show that the unate cascade functions uniquely achieve the absolute minimum APL.
Type
Article
Description
IEEE Transactions on Computers, Vol. 54, No.9, pp.1041-1053, Sept. 2005.
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. As such, it is in the public domain, and under the provisions of Title 17, United States Code, Section 105, may not be copyrighted.
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. As such, it is in the public domain, and under the provisions of Title 17, United States Code, Section 105, may not be copyrighted.
Series/Report No
Department
Department of Electric and Computer Engineering
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Citation
J. T. Butler, T. Sasao, and M. Matsuura, “Average path length of binary decision diagrams" IEEE Transactions on Computers, Vol. 54, No.9, pp.1041-1053, Sept. 2005.