Abstract
We present an efficient reduction mapping undirected graphs G with n = 2k 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.
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Kristensen, J.T., Miltersen, P.B. (2006). Finding Small OBDDs for Incompletely Specified Truth Tables Is Hard. In: Chen, D.Z., Lee, D.T. (eds) Computing and Combinatorics. COCOON 2006. Lecture Notes in Computer Science, vol 4112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11809678_51
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DOI: https://doi.org/10.1007/11809678_51
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