Abstract
An ordered binary decision diagram (OBDD) is a graph representation of a Boolean function, and it is considered as a restricted branching program. According to its good properties, an OBDD is widely used in computer aided logic design. In this paper, the size of ordered binary decision diagrams representing threshold functions is discussed. First, we prove an Ω(n2cn1-ε) lower bound on the OBDD size necessary to represent any threshold function when the variable ordering can be chosen adaptively to minimize the OBDD size. Next, we show that it is not possible to find a good variable ordering only from the total order of weights, that is, for any variable ordering of this kind, there exists a threshold function that requires an exponential size OBDD, but is represented in polynomial size by the optimal variable ordering.
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© 1997 Springer-Verlag Berlin Heidelberg
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Takenaga, Y., Nouzoe, M., Yajima, S. (1997). Size and variable ordering of OBDDs representing threshold functions. In: Jiang, T., Lee, D.T. (eds) Computing and Combinatorics. COCOON 1997. Lecture Notes in Computer Science, vol 1276. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0045076
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DOI: https://doi.org/10.1007/BFb0045076
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