The conceptions of χ-value and K-rotation symmetric Boolean functions are introduced by Cusick. K-rotation symmetric Boolean functions are a special rotation symmetric functions, which are invariant under the k − th power of ρ. In this paper, we discuss cubic 2-value 2-rotation symmetric Boolean function with 2n variables, which denoted by F2n(x2n). We give the recursive formula of weight of F2...

In this research report, we propose an enhancement of the compilation of synchronous programs with a combined numerical-Boolean abstraction. While our approach applies to synchronous dataflow languages in general, here, we consider the Signal language for illustration. In the new abstraction, every signal in a program is associated with a pair of the form (clock, value), where clock is a Boolea...

A function f : {−1, 1} → R is called pseudo-Boolean. It is wellknown that each pseudo-Boolean function f can be written as f(x) =

The correlation of a Boolean functions with its spectral coefficients is closely related to the some cryptosystems and applications in engineering and computer sciences. By analysis of Boolean functions can be investigated whether a given function belongs to some standard class (linear, non-linear self-dual, threshold etc.) functions. For n variable Boolean function the number of nonzero spectr...

Interaction graphs provide an important qualitative modeling approach for System Biology. This paper presents a novel approach for construction of interaction graph with the help of Boolean function decomposition. Each decomposition part (Consisting of 2-bits) of the Boolean functions has some important significance. In the dynamics of a biological system, each variable or node is nothing but g...

We consider an n-ary random Boolean function f such that Pr[f(α̃) = 1] = p for α̃ ∈ {0, 1} and study its geometric model, the so called interval graph. The interval graph of a Boolean function was introduced by Sapozhenko and has been used in construction of schemes realizing Boolean functions. Using this model, we estimate the number of maximal intervals intersecting a given maximal interval of ...

For a Boolean Matrix A a binary vector v is called tfrequent if Av has at least t entries of value supp (v). Given two parameters t1 < t2 the t1-frequent but t2-infrequent vectors of a matrix represent a Boolean function that has two domains of (opposite) monotonicity. These functions were studied for the purpose of data analysis and abstract concept discovery in (Eisenschmidt et al. 2010). In ...

A Boolean circuit C on n inputs x1, . . . , xn is a directed acyclic graph (DAG) with n nodes of in-degree 0 (the inputs x1, . . . , xn), one node of out-degree 0 (the output), and every node of the graph except the input nodes is labeled by AND, OR, or NOT; it has in-degree 2 (for AND and OR), or 1 (for NOT). The Boolean circuit C computes a Boolean function f(x1, . . . , xn) in the obvious wa...

Although there are plenty of AutoCAD books available for architects, interior designers, and engineers, it has been difficult for the author to find an appropriate textbook for students who major in interior design while teaching AutoCAD, especially 3-D AutoCAD at the sophomore level. Most existing 3-D AutoCAD textbooks are more engineering oriented. Industrial machine components such as bolts ...

Nested canalyzing functions have been studied recently in the context of Boolean network models of gene regulatory networks. This paper provides a parametrization for the class of nested canalyzing functions by the points of an algebraic variety over the field with two elements. This variety is defined by the set of relations that the coefficients of such a function need to satisfy. This set of...