Polyabelian loops and Boolean completeness

Francois Lemieux, Cristopher Moore, and Denis Therien

Commentationes Mathematicae Universitatis Carolinae 41 (2000) 671-686, the proceedings of Loops '99.

This is a purely algebraic version of our paper ``Circuits and expressions with non-associative gates.'' We generalize the notion of solvability for non-associative algebras to something we call ``polyabelianness', and show that a loop is Boolean-complete --- that is, capable of simulating arbitrary Boolean functions --- if and only if it is not polyabelian.

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Cris Moore <moore@santafe.edu>