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In this paper an algorithm is designed which generates in-equivalent Boolean functions of any number of variables from the four Boolean functions of single variable. The grammar for such set of Boolean function is provided. The Turing Machine that accepts such set is constructed.
Classification of Non-linear Boolean functions is a long-standing problem in the area of theoretical computer science. In this paper, effort has been made to achieve a systematic classification of all n-variable Boolean functions, where only one affi
A pairing function J associates a unique natural number z to any two natural numbers x,y such that for two unpairing functions K and L, the equalities K(J(x,y))=x, L(J(x,y))=y and J(K(z),L(z))=z hold. Using pairing functions on natural number represe
We study the volatility of the output of a Boolean function when the input bits undergo a natural dynamics. For $n = 1,2,ldots$, let $f_n:{0,1}^{m_n} ra {0,1}$ be a Boolean function and $X^{(n)}(t)=(X_1(t),ldots,X_{m_n}(t))_{t in [0,infty)}$ be a vec
The subject of this textbook is the analysis of Boolean functions. Roughly speaking, this refers to studying Boolean functions $f : {0,1}^n to {0,1}$ via their Fourier expansion and other analytic means. Boolean functions are perhaps the most basic o
We consider the extensions of modal transition systems (MTS), namely Boolean MTS and parametric MTS and we investigate the refinement problems over both classes. Firstly, we reduce the problem of modal refinement over both classes to a problem solvab