Geodesic
A lower bound for the computational complexity of a set of disjunctives in a monotone basis
Zapiski Nauchnykh Seminarov POMI, Theoretical application of methods of mathematical logic. Part II, Tome 68 (1977), pp. 19-25

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A set of disjunctions of some variables is constructed and a nonlinear lower bound is proved for the circuit complexity of this set in systems of functional elements (s.f.e.) in a fixed monotone basis. The proposed method for proving the lower bound of circuit complexity in the s.f.e. differs from previously known methods (in a monotone basis). 
@article{ZNSL_1977_68_a1,
     author = {D. Yu. Grigor'ev},
     title = {A lower bound for the computational complexity of a set of disjunctives in a monotone basis},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {19--25},
     publisher = {mathdoc},
     volume = {68},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1977_68_a1/}
}
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D. Yu. Grigor'ev. A lower bound for the computational complexity of a set of disjunctives in a monotone basis. Zapiski Nauchnykh Seminarov POMI, Theoretical application of methods of mathematical logic. Part II, Tome 68 (1977), pp. 19-25. http://geodesic.mathdoc.fr/item/ZNSL_1977_68_a1/