On the hardness of approximating the minimum consistent OBDD problem

  • Kouichi Hirata
  • Shinichi Shimozono
  • Ayumi Shinohara
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1097)


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 nε 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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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Kouichi Hirata
    • 1
  • Shinichi Shimozono
    • 2
  • Ayumi Shinohara
    • 3
  1. 1.Department of Artificial IntelligenceKyushu Institute of TechnologyIizukaJapan
  2. 2.Department of Control Engineering and ScienceKyushu Institute of TechnologyIizukaJapan
  3. 3.Research Institute of Fundamental Information ScienceKyushu UniversityFukuokaJapan

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