18,426 research outputs found
Landscape Boolean Functions
In this paper we define a class of Boolean and generalized Boolean functions
defined on with values in (mostly, we consider
), which we call landscape functions (whose class containing generalized
bent, semibent, and plateaued) and find their complete characterization in
terms of their components. In particular, we show that the previously published
characterizations of generalized bent and plateaued Boolean functions are in
fact particular cases of this more general setting. Furthermore, we provide an
inductive construction of landscape functions, having any number of nonzero
Walsh-Hadamard coefficients. We also completely characterize generalized
plateaued functions in terms of the second derivatives and fourth moments.Comment: 19 page
Join-irreducible Boolean functions
This paper is a contribution to the study of a quasi-order on the set
of Boolean functions, the \emph{simple minor} quasi-order. We look at
the join-irreducible members of the resulting poset . Using a
two-way correspondence between Boolean functions and hypergraphs,
join-irreducibility translates into a combinatorial property of hypergraphs. We
observe that among Steiner systems, those which yield join-irreducible members
of are the -2-monomorphic Steiner systems. We also describe
the graphs which correspond to join-irreducible members of .Comment: The current manuscript constitutes an extension to the paper
"Irreducible Boolean Functions" (arXiv:0801.2939v1
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