The computation of characteristic vectors of logical-probabilistic expressions
The conjunction of a particular form of majority logic functions and some of its properties
The logic of neural networks.
This paper establishes the equivalence between multilayer feedforward networks and linear combinations of Lukasiewicz propositions. In this sense, multilayer forward networks have a logic interpretation, which should permit to apply logical techniques in the neural networks framework.
The Number of Non-Isomorphic Hamiltonian Circuits in an -Dimensional Cube
The semigroup of circulant Boolean matrices
The spectral test of the Boolean function linearity
The paper discusses the problem of recognizing the Boolean function linearity. A spectral method of the analysis of Boolean functions using the Walsh transform is described. Linearity and nonlinearity play important roles in the design of digital circuits. The analysis of the distribution of spectral coefficients allows us to determine various combinatorial properties of Boolean functions, such as redundancy, monotonicity, self-duality, correcting capability, etc., which seems more difficult be...
Towards a characterization of bipartite switching classes by means of forbidden subgraphs
We investigate which switching classes do not contain a bipartite graph. Our final aim is a characterization by means of a set of critically non-bipartite graphs: they do not have a bipartite switch, but every induced proper subgraph does. In addition to the odd cycles, we list a number of exceptional cases and prove that these are indeed critically non-bipartite. Finally, we give a number of structural results towards proving the fact that we have indeed found them all. The search for critically...
Type et graphe des distances d'une fonction booléenne