Geodesic
Functions from Schaefer classes having negations belonging to other Schaefer classes
Matematičeskie voprosy kriptografii, Tome 6 (2015), pp. 23-48

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Multiaffine, bijunctive ($2$-CNF), weakly positive and weakly negative (Horn's) Boolean functions generates polynomially solvable systems of equations. These sets of Boolean functions are called the Schaefer classes. We describe sets of Boolean functions $f$ from any Schaefer class such that $f$ belongs to another Schaefer class. The results obtained may be applied to the solution of systems of Boolean equations. 
@article{MVK_2015_6_a1,
     author = {S. P. Gorshkov},
     title = {Functions from {Schaefer} classes having negations belonging to other {Schaefer} classes},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {23--48},
     publisher = {mathdoc},
     volume = {6},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2015_6_a1/}
}
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S. P. Gorshkov. Functions from Schaefer classes having negations belonging to other Schaefer classes. Matematičeskie voprosy kriptografii, Tome 6 (2015), pp. 23-48. http://geodesic.mathdoc.fr/item/MVK_2015_6_a1/