The size of reduced OBDD´s and optimal read-once branching programs for almost all Boolean functions

Author

Wegener, Ingo

Author_Institution

Dept. of Comput. Sci., Dortmund Univ., Germany

Volume

43

Issue

11

fYear

1994

fDate

11/1/1994 12:00:00 AM

Firstpage

1262

Lastpage

1269

Abstract

Boolean functions are often represented by ordered binary-decision diagrams (OBDDs) introduced by Bryant (1986). Liaw and Lin (1992) have proved upper and lower bounds on the minimal OBDD size of almost all Boolean functions. Now tight bounds are proved for the minimal OBDD size for arbitrary or optimal variable orderings and for the minimal read-once branching program size of almost all functions. Almost all Boolean functions have a sensitivity of almost 1, i.e., the minimal OBDD size for an optimal variable ordering differs from the minimal OBDD size for a worst variable ordering by a factor of at most 1+ε(n) where ε(n) converges exponentially fast to 0

Keywords

Boolean functions; computational complexity; directed graphs; programming theory; Boolean functions; minimal read-once branching program size; optimal read-once branching programs; ordered binary-decision diagrams; reduction rules; size complexity; variable ordering; Algorithm design and analysis; Binary decision diagrams; Boolean functions; Data structures; Design automation; Logic design; Merging; Test pattern generators; Testing;

fLanguage

English

Journal_Title

Computers, IEEE Transactions on

Publisher

ieee

ISSN

0018-9340

Type

jour

DOI

10.1109/12.324559

Filename

324559