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Paper:

TR06-004 | 6th January 2006 00:00

Finding small OBDDs for incompletely specified truth tables is hard

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TR06-004
Authors: Jesper Torp Kristensen, Peter Bro Miltersen
Publication: 10th January 2006 09:05
Downloads: 1200
Keywords: 


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}^(4k+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.



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