On composition-closed classes of Boolean functions

Details On composition-closed classes of Boolean functions On composition-closed classes of Boolean functions

2011-02-21

arxiv.org/abs/1102.4355v1

Mathematics

Rings and Algebras

20 pages, 8 figures

Scientific paper

We determine all composition-closed equational classes of Boolean functions. These classes provide a natural generalization of clones and iterative algebras: they are closed under composition, permutation and identification (diagonalization) of variables and under introduction of inessential variables (cylindrification), but they do not necessarily contain projections. Thus the lattice formed by these classes is an extension of the Post lattice. The cardinality of this lattice is continuum, yet it is possible to describe its structure to some extent.

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