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Abstract: We study the Fourier representation of Boolean functions. The goal is to look at the frequency domain of Boolean functions to get complexity properties. Preliminary results indicate that this might be fruitful. In addition to presenting new results, we review some of the most significant work on the subject. Istituto di Matematica Computazionale, Consiglio Nazionale delle Ricerche, and Dipartimento di Informatica, Pisa (Italy). y Istituto di Matematica Computazionale, Consiglio Nazionale delle... (Update)
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...are not. The average sensitivity is a finer characteristic of Boolean functions which has been studied in a number of papers, see [2, 5, 14]. Our main result consists in a linear lower bound on the average sensitivity of testing square free numbers. More precisely, we...
.... coefficients of Boolean functions and their complexity characteristics have been studied in a number of works, see [2 5, 8, 14, 20, 21, 24, 25]. In particular, these spectral techniques have been successfully applied to the parity function and to threshold functions....
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BibTeX entry: (Update)
A. Bernasconi, B. Codenotti and J. Simon, `On the Fourier analysis of Boolean functions', Preprint (1996), 1-24. http://citeseer.ist.psu.edu/bernasconi96fourier.html More
@misc{ bernasconi96fourier,
author = "A. Bernasconi and B. Codenotti and J. Simon",
title = "the Fourier analysis of Boolean functions",
text = "A. Bernasconi, B. Codenotti and J. Simon, `On the Fourier analysis of Boolean
functions', Preprint (1996), 1-24.",
year = "1996",
url = "citeseer.ist.psu.edu/bernasconi96fourier.html" }
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59 The Influence of Variables on Boolean Functions (context) - Kahn, Kalai et al. - 1988
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18 A Spectral Lower Bound Technique for the Size of Decision Tr.. (context) - Brandman, Orlitsky et al. - 1990
18 Amplification of Probabilistic Boolean Formulas (context) - Boppana - 1989
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15 The Harmonic Sieve: A Novel Application of Fourier Analysis .. (context) - Jackson - 1995
15 Polynomial Threshold Functions (context) - Bruck, Smolensky - 1992
15 Harmonic Analysis of Switching Functions (context) - Lechner - 1971
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6 and Parallel Complexity (context) - Clote, Kranakis et al. - 1991
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5 Spectral Properties of threshold functions (context) - Gotsman, Linial - 1994
5 Amplification and Percolation - Dubiner, Zwick - 1997
3 Measures of Boolean Function Complexity based on Harmonic An.. (context) - Bernasconi, Codenotti - 1994
3 The Computational Complexity of the Circuit Value and Networ.. (context) - Subramanian - 1990
2 Symmetric Functions in AC 0 can be Computed in Constant Dept.. (context) - Wegener, Wurm et al. - 1992
2 Spectral Method of Boolean Function Complexity (context) - Hurst, Miller et al. - 1982
1 Technical Report TR-93-030 International Computer Science In.. (context) - Bernasconi, Codenotti et al. - 1993
1 Improvements on Khrapchenko's Theorem (context) - Koutsoupias - 1993
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