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On the size of ordered binary decision diagrams representing threshold functions

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Algorithms and Computation (ISAAC 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 834))

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Abstract

An ordered binary decision diagram (OBDD) is a graph representation of a Boolean function. In this paper, the size of ordered binary decision diagrams representing threshold functions is discussed. We consider two cases: the case when an ordering of variables is given and the case when it is adaptively chosen. We show 1) O(2n/2) upper bound for both cases, 2) Ω(2n/2) lower bound for the former case and 3) Ω(n2√n/2) lower bound for the latter case.

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References

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Authors and Affiliations

  1. Department of Information Science, Faculty of Engineering, Kyoto University, 606-01, Kyoto, Japan

    Kazuhisa Hosaka, Yasuhiko Takenaga & Shuzo Yajima

Authors
  1. Kazuhisa Hosaka
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  2. Yasuhiko Takenaga
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  3. Shuzo Yajima
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Editor information

Ding-Zhu Du Xiang-Sun Zhang

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© 1994 Springer-Verlag Berlin Heidelberg

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Hosaka, K., Takenaga, Y., Yajima, S. (1994). On the size of ordered binary decision diagrams representing threshold functions. In: Du, DZ., Zhang, XS. (eds) Algorithms and Computation. ISAAC 1994. Lecture Notes in Computer Science, vol 834. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58325-4_226

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  • DOI: https://doi.org/10.1007/3-540-58325-4_226

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58325-7

  • Online ISBN: 978-3-540-48653-4

  • eBook Packages: Springer Book Archive

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