Local Maxima of Quadratic Boolean Functions

Generalised Bent Criteria for Boolean Functions (I)

Generalisations of the bent property of a boolean function are presented, by proposing spectral analysis with respect to a well-chosen set of local unitary transforms. Quadratic boolean functions are related to simple graphs and it is shown that the orbit generated by successive Local Complementations on a graph can be found within the transform spectra under investigation. The flat spectra of ...

On Self-Dual Quantum Codes, Graphs, and Boolean Functions

A short introduction to quantum error correction is given, and it is shown that zero-dimensional quantum codes can be represented as self-dual additive codes over GF(4) and also as graphs. We show that graphs representing several such codes with high minimum distance can be described as nested regular graphs having minimum regular vertex degree and containing long cycles. Two graphs correspond ...

Persistency for higher-order pseudo-boolean maximization

A pseudo-Boolean function is a function from a 0/1-vector to the reals. Minimizing pseudo-Boolean functions is a very general problem with many applications. In image analysis, the problem arises in segmentation or as a subroutine in task like stero estimation and image denoising. Recent years have seen an increased interest in higher-degree problems, as opposed to quadratic pseudo-Boolean func...

Expected Number of Local Maxima of Some Gaussian Random Polnomials

Spectral Properties of Boolean Functions, Graphs and Graph States

Generalisations of the bent property of a Boolean function are presented, by proposing spectral analysis of the Boolean function with respect to a well-chosen set of local unitary transforms. Quadratic Boolean functions are related to simple graphs and it is shown that the orbit generated by some graph transforms can be found within the spectra of certain unitary transform sets. The flat spectr...