Abstract
Coudert made a breakthrough in the two-level logic minimization problem with Ordered Binary Decision Diagrams (OBDDs, in short) recently [3]. This paper discusses relationship between the two OBDDs of a monotone function and of 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.
Part of this research was performed while the first author was at Department of Information Science, University of Tokyo.
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© 1996 Springer-Verlag Berlin Heidelberg
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Hayase, K., Imai, H. (1996). OBDDs of a monotone function and of its prime implicants. In: Asano, T., Igarashi, Y., Nagamochi, H., Miyano, S., Suri, S. (eds) Algorithms and Computation. ISAAC 1996. Lecture Notes in Computer Science, vol 1178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0009489
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DOI: https://doi.org/10.1007/BFb0009489
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