Extending Semilattices Is Hard
We show that the semilattice extension problem raised by Arbib and Manes in  is NP-hard, implying that no simple solution is likely to be forthcoming.
G. Markowsky, "Extending Semilattices Is Hard," Algebra Universalis, vol. 17, no. 1, pp. 406-407, Springer Verlag, Dec 1983.
The definitive version is available at http://dx.doi.org/10.1007/BF01194547
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