Finding Small OBDDs for Incompletely Specified Truth Tables Is Hard [chapter]

Jesper Torp Kristensen, Peter Bro Miltersen
2006 Lecture Notes in Computer Science  
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
more » ... hard to approximate. 1 Very similar results were obtained by Pitt and Warmuth [11] and Simon [14] for deterministic finite automata, a model closely related to OBDDs.
doi:10.1007/11809678_51 fatcat:2nsco5zy5vgyzex3jsfzxjny6i