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On the hardness of approximating the minimum consistent OBDD problem

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Book cover Algorithm Theory — SWAT'96 (SWAT 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1097))

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Abstract

Ordered binary decision diagrams (OBDDs, for short) represent Boolean functions as directed acyclic graphs. The minimum consistent OBDD problem is, given an incomplete truth table of a function, to find the smallest OBDD that is consistent with the truth table with respect to a fixed order of variables. We show that this problem is NP-hard, and prove that there is a constant ε > 0 such that no polynomial time algorithm can approximate the minimum consistent OBDD within the ratio n ε unless P=NP, where n is the number of variables. This result suggests that OBDDs are unlikely to be polynomial time learnable in PAC-learning model.

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Author information

Authors and Affiliations

  1. Department of Artificial Intelligence, Kyushu Institute of Technology, Kawazu 680-4, 820, Iizuka, Japan

    Kouichi Hirata

  2. Department of Control Engineering and Science, Kyushu Institute of Technology, Kawazu 680-4, 820, Iizuka, Japan

    Shinichi Shimozono

  3. Research Institute of Fundamental Information Science, Kyushu University, 812, Fukuoka, Japan

    Ayumi Shinohara

Authors
  1. Kouichi Hirata
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  2. Shinichi Shimozono
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  3. Ayumi Shinohara
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Rolf Karlsson Andrzej Lingas

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© 1996 Springer-Verlag Berlin Heidelberg

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Hirata, K., Shimozono, S., Shinohara, A. (1996). On the hardness of approximating the minimum consistent OBDD problem. In: Karlsson, R., Lingas, A. (eds) Algorithm Theory — SWAT'96. SWAT 1996. Lecture Notes in Computer Science, vol 1097. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61422-2_125

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  • DOI: https://doi.org/10.1007/3-540-61422-2_125

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61422-7

  • Online ISBN: 978-3-540-68529-6

  • eBook Packages: Springer Book Archive

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