OBDDs of a Monotone Function and Its Prime Implicants |
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Authors: | K Hayase H Imai |
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Affiliation: | (1) NTT Multimedia Networks Laboratories, 1-1 Hikarinooka, Yokosuka-Shi 239, Japan hayase@nttmhs.tnl.ntt.co.jp , JP;(2) Department of Information Science, University of Tokyo, Hongo, Tokyo 113, Japan imai@is.s.u-tokyo.ac.jp, JP |
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Abstract: | Coudert made a breakthrough in the two-level logic minimization problem with Ordered Binary Decision Diagrams (OBDDs for
short) recently 3]. This paper discusses the relationship between the two OBDDs of a monotone function and its prime implicant
set to clarify the complexity of this practically efficient method. We show that there exists a monotone function which has
an O(n) size sum-of-products but cannot be represented by a polynomial size OBDD. In other words, we cannot obtain the OBDD of the
prime implicant set of a monotone function in an output-size sensitive manner once we have constructed the OBDD of that function as in 3], in the worst case. A positive result is also given for a meaningful
class of matroid functions.
Received April 1997, and in revised form December 1997, and in final form February 1998. |
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