Separating points by parallel hyperplanes--characterization problem

Characterization of Linearly Separable Boolean Functions: A Graph-Theoretic Perspective

In this paper, we present a novel approach for studying Boolean function in a graph-theoretic perspective. In particular, we first transform a Boolean function f of n variables into an induced subgraph H_f of the n -dimensional hypercube, and then, we show the properties of linearly separable Boolean functions on the basis of the analysis of the structure of H_f . We define a new class of graphs, called hyperstar, and prove that the induced subgraph H_f of any linearly separable Boolean function f is a hyperstar. The proposal of hyperstar helps us uncover a number of fundamental properties of linearly separable Boolean functions in this paper.

The correspondence between deterministic and stochastic digital neurons: analysis and methodology

This paper analyzes the criteria for the direct correspondence between a deterministic neural network and its stochastic counterpart, and presents the guidelines that have been derived to establish such a correspondence during the design of a neural network application. In particular, the role of the slope and bias of the neuron activation function and that of the noise of its output have been addressed, thus filling a specific literature gap. This paper presents the results that have been theoretically derived in this regard, together with the simulations of few relevant application examples that have been performed to support them.