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Electronic Colloquium on Computational Complexity

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TR99-048 | 7th December 1999 00:00

Asymptotically Optimal Bounds for OBDDs and the Solution of Some Basic OBDD Problems



Ordered binary decision diagrams (OBDDs) are nowadays the
most common dynamic data structure or representation type
for Boolean functions. Among the many areas of application
are verification, model checking, and computer aided design.
For many functions it is easy to estimate the OBDD size but
asymptotically optimal bounds are only known in simple situations.
In this paper, methods for proving asymptotically optimal bounds
are presented and applied to the solution of some basic problems
concerning OBDDs. The largest size increase by a synthesis step
of $\pi$-OBDDs followed by an optimal reordering is determined as
well as the largest ratio of the size of deterministic finite
automata, quasi-reduced OBDDs, and zero-suppressed BDDs compared
to the size of OBDDs. Moreover, the worst case OBDD size of
functions with a given number of $1$-inputs is investigated.

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