2 Probabilistic modelling of learning 4 2.1 A probabilistic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 A learnability result for Boolean classes . . . . . . . . . . . . . . . . . . . . 6 2.4 Learning monomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.5 Di...

In this paper, we obtain the cross-correlation spectrum of generalized bent Boolean functions in a subclass of MaioranaMcFarland class (GMMF). An affine transformation which preserve the cross-correlation spectrum of two generalized Boolean functions, in absolute value is also presented. A construction of generalized bent Boolean functions in (n+ 2) variables from four generalized Boolean funct...

in this paper, we define and study the notion of the real-valued functions on a frame $l$. we show that $f(l) $, consisting of all frame homomorphisms from the power set of $mathbb{r}$ to a frame $ l$, is an $f$-ring, as a generalization of all functions from a set $x$ into $mathbb r$. also, we show that $f(l) $ is isomorphic to a sub-$f$-ring of $mathcal{r}(l)$, the ring of real-valued continu...

In this paper, we present a new type of neuron, called Boolean neuron. Further, we suggest the general structure of a neural network that includes only Boolean neurons and may realize several sets of Boolean functions. The advantages of these neural networks consist in the reduction of memory space and computation time in comparison to the representation of Boolean functions by usual neural net...