Abstract
An Ordered Binary Decision Diagram (OBDD) is a directed acyclic graph representing a Boolean function. The size of OBDDs largely depends on the variable ordering. In this paper, we show the size of the OBDD representing the i-th bit of the output of n-bit/n-bit integer division is Ω(2(n-i)/8) for any variable ordering. We also show that V-OBDDs, Λ-OBDDs and ⊕-OBDDs representing integer division has the same lower bounds on the size. We develop new methods for proving lower bounds on the size of V-OBDDs, Λ-OBDDs and ⊕-OBDDs.
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© 1997 Springer-Verlag Berlin Heidelberg
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Horiyama, T., Yajima, S. (1997). Exponential lower bounds on the size of OBDDs representing integer division. In: Leong, H.W., Imai, H., Jain, S. (eds) Algorithms and Computation. ISAAC 1997. Lecture Notes in Computer Science, vol 1350. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63890-3_19
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DOI: https://doi.org/10.1007/3-540-63890-3_19
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