Walsh Coefficients Distribution
نویسنده
چکیده
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 spectral coefficients can be 2 in the worst case. However many interesting classes of Boolean functions have more compact representations. In this paper Boolean functions which small number of significant spectral coefficients have been investigated. Particularly functions with k n 4 = and 8 k = nonzero coefficients have been constructed.
منابع مشابه
Evaluation of Psychometric Properties of Walsh Family Resilience Questionnaire
Background: Considering the importance of family resilience and the broader range of applications that focus on the resilience of families, in the current study, the introduction of resilience structure of the family has been identified as an essential research demand. Therefore, consideration of the psychometric properties of the most widely used tools in this area, including family resilience...
متن کاملOn the Fourier-walsh Spectrum of the Moebius Function
We study the Fourier-Walsh spectrum {μ̂(S);S ⊂ {1, . . . , n}} of the Moebius function μ restricted to {0, 1, 2, . . . , 2 − 1} ≃ {0, 1} and prove that it is not captured by levels {μ̂(S)| |S| < n 2 3 −ε}. An application to correlation with monotone Bolean functions is given. 0. Introduction This paper may be seen as a companion of [B1] on the behavior of the Fourier-Walsh coefficients of the Moe...
متن کاملThe decay of the Walsh coefficients of smooth functions
We give upper bounds on the Walsh coefficients of functions for which the derivative of order at least one has bounded variation of fractional order. Further, we also consider the Walsh coefficients of functions in periodic and non-periodic reproducing kernel Hilbert spaces. A lower bound which shows that our results are best possible is also shown. Mathematical Subject Classification (2000): P...
متن کاملA Tractable Walsh Analysis of SAT and its Implications for Genetic Algorithms
Walsh Transforms measure all sources of nonlinear interactions for functions that have a bit representation. There can be exponentially many nonlinear interactions and exactly computing all Walsh coefficients is usually intractable for non-trivial functions. In this paper we will show that SAT problems evaluated as MAXSAT functions have a highly restricted set of nonzero Walsh coefficients and ...
متن کاملInequalities for Walsh Polynomials with Semi-monotone and Semi-convex Coefficients
Using the concept of majorant sequences (see [4, ch. XXI], [5], [7], [8]) some new inequalities for Walsh polynomials with complex semi-monotone, complex semi-convex, complex monotone and complex convex coefficients are given.
متن کامل