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Least Upper Bounds on OBDD Sizes
June 1994 (vol. 43 no. 6)
pp. 764-767

This paper derives exact equations for the maximum number of nonterminal vertexes in reduced and quasi-reduced ordered binary decision diagrams (OBDD's). A reduced OBDD is reduced by both merging and deleting vertices, and a quasi-reduced OBDD is reduced only by merging. These formulas are used to tighten Lee's original bounds, and to correct the bounds recently reported by H.T. Liaw and C.S. Lin (1992).

[1] C. Y. Lee, "Representation of switching circuits by binary-decision programs,"Bell Syst. Tech. J., vol. 38, no. 7, pp. 985-999, July 1959.
[2] H.-T. Liaw and C.-S. Lin, "On the OBDD-representation of general Boolean functions,"IEEE Trans. Comput., vol. 41, no. 6, pp. 661-664, 1992.
[3] R. E. Bryant, "Graph-based algorithms for Boolean function manipulation,"IEEE Trans. Comput., vol. C-35, no. 8, pp. 677-691, Aug. 1986.

Index Terms:
decoding; Boolean functions; least upper bounds; OBDD sizes; exact equations; nonterminal vertexes; reduced ordered binary decision diagrams.
M.A. Heap, M.R. Mercer, "Least Upper Bounds on OBDD Sizes," IEEE Transactions on Computers, vol. 43, no. 6, pp. 764-767, June 1994, doi:10.1109/12.286311
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