Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
The minimum consistent DFA problem cannot be approximated within any polynomial
Journal of the ACM (JACM)
Free Bits, PCPs, and Nonapproximability---Towards Tight Results
SIAM Journal on Computing
On the hardness of approximating the minimum consistent acyclic DFA and decision diagram
Information Processing Letters
Zero knowledge and the chromatic number
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
Symbolic manipulation of Boolean functions using a graphical representation
DAC '85 Proceedings of the 22nd ACM/IEEE Design Automation Conference
On the Hardness of Approximating the Minimum Consistent OBDD Problem
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
Towards optimal lower bounds for clique and chromatic number
Theoretical Computer Science
Improved Inapproximability Results for MaxClique, Chromatic Number and Approximate Graph Coloring
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
On the complexity of minimizing the OBDD size for incompletely specified functions
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Analysis of a genetic programming algorithm for association studies
Proceedings of the 10th annual conference on Genetic and evolutionary computation
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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)n2 + 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.