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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)

Abstract

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.

Keywords

Boolean Function Chromatic Number Truth Table Decision Node Binary Decision Diagram 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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