Set-reconstructibility of Post classes
Couceiro, Miguel; Lehtonen, Erkko; Schölzel, Karsten
Discrete Applied Mathematics, 187 (2015), 12–18
http://dx.doi.org/10.1016/j.dam.2015.02.013
The clones of Boolean functions are classified in regard to set-reconstructibility via a strong dichotomy result: the clones containing only affine functions, conjunctions, disjunctions or constant functions are set-reconstructible, whereas the remaining clones are not weakly reconstructible.
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