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by noajshu 2558 days ago
The monotone, linear, etc. functions are called clones and the clones form a lattice called Post's Lattice

https://en.wikipedia.org/wiki/Post%27s_lattice

Given several logic gates, if their most recent common ancestor in the lattice is the clone of all boolean functions, then that set is universal. This provides a convenient prescription for deciding universality for a new k-input gate.