Exponential lower bounds on the size of OBDDs representing integer division

  • Takashi Horiyama
  • Shuzo Yajima
Session 4A
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1350)


An Ordered Binary Decision Diagram (OBDD) is a directed acyclic graph representing a Boolean function. The size of OBDDs largely depends on the variable ordering. In this paper, we show the size of the OBDD representing the i-th bit of the output of n-bit/n-bit integer division is Ω(2 (n-i)/8 ) for any variable ordering. We also show that V-OBDDs, Λ-OBDDs and ⊕-OBDDs representing integer division has the same lower bounds on the size. We develop new methods for proving lower bounds on the size of V-OBDDs, Λ-OBDDs and ⊕-OBDDs.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Takashi Horiyama
    • 1
  • Shuzo Yajima
    • 2
  1. 1.Dept. of Information Science, Graduate School of EngineeringKyoto UniversityKyotoJapan
  2. 2.Faculty of InformaticsKansai UniversityOsakaJapan

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