Finding Small OBDDs for Incompletely Specified Truth Tables Is Hard

  • Jesper Torp Kristensen
  • Peter Bro Miltersen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4112)


We present an efficient reduction mapping undirected graphs G with n = 2 k vertices for integers k to tables of partially specified Boolean functions g: {0,1}\(^{\rm 4{\it k}+1}\) →{0,1,⊥} so that for any integer m, G has a vertex colouring using m colours if and only if g has a consistent ordered binary decision diagram with at most (2m + 2)n 2 + 4n decision nodes. From this it follows that the problem of finding a minimum-sized consistent OBDD for an incompletely specified truth table is NP-hard and also hard to approximate.


Boolean Function Chromatic Number Truth Table Decision Node Binary Decision Diagram 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jesper Torp Kristensen
    • 1
  • Peter Bro Miltersen
    • 1
  1. 1.Department of Computer ScienceUniversity of AarhusDenmark

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