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We consider the question of which loops are capable of expressing arbitrary Boolean functions through expressions of constants and variables. We call this property . It is a generalization of functional completeness, and is intimately connected to the computational complexity of various questions about expressions, circuits, and equations defined over the loop. We say that a loop is if it is an iterated affine quasidirect product of Abelian groups; polyabelianness coincides with solvability for...
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