When does a generalized Boolean quasiring become a Boolean ring?

Omega-almost Boolean rings

In this paper the concept of an $Omega$- Almost Boolean ring is introduced and illistrated how a sheaf of algebras can be constructed from an $Omega$- Almost Boolean ring over a locally Boolean space.

Boolean Ring Satisfiability

We propose a method for testing satisfiability based on Boolean rings. It makes heavy use of simplification, but avoids the potential size increase associated with application of the distributive law by employing a combined linear and binomial representation. Several complexity results suggest why the method may be relatively effective in many cases. The framework is also amenable to learning f...

Octal Generalized Boolean Functions

In this paper we characterize (octal) bent generalized Boolean functions defined on Z2 with values in Z8. Moreover, we propose several constructions of such generalized bent functions for both n even and n odd.

Generalized Boolean Bent Functions

The notions of perfect nonlinearity and bent functions are closely dependent on the action of the group of translations over IF2 . Extending the idea to more generalized groups of involutions without fixed points gives a larger framework to the previous notions. In this paper we largely develop this concept to define G-perfect nonlinearity and G-bent functions, where G is an Abelian group of in...

Boolean Constraint Satisfaction Problems: When Does Post's Lattice Help?