A. Bernasconi, `On the complexity of balanced Boolean functions', Information Processing Letters, 70 (1999), 157-163. Home/Search Document Not in Database Summary Related Articles Check |
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Communication Complexity And Fourier Coefficients Of The.. - Shparlinski (2000) (1 citation) (Correct)
.... relations between Fourier coe#cients and various complexity characteristics such as such as the circuit complexity, the average sensitivity, the formula size, the average decision tree depth, the degrees of exact and approximate polynomial representations over the reals and several others, see [3, 4, 8, 15, 22, 23, 27] and references therein. We remark, that although these results do not seem to have any cryptographic implications it is still interesting to study complexity characteristics of such an attractive number theoretic function. Various complexity lower bounds for Boolean functions associated with ....
A. Bernasconi, `On the complexity of balanced Boolean functions', Inform. Proc. Letters, 70 (1999), 157--163.
On the Complexity of Some Arithmetic Problems over F2[T] - Allender, Bernasconi, Damm, .. Self-citation (Bernasconi) (Correct)
No context found.
A. Bernasconi, `On the complexity of balanced Boolean functions', Information Processing Letters, 70 (1999), 157-163.
Circuit and Decision Tree Complexity of Some Number.. - Bernasconi, Damm.. (1998) (1 citation) Self-citation (Bernasconi) (Correct)
....based on the Abstract Harmonic Analysis on the hypercube have been shown to represent a very useful tool for obtaining lower complexity bounds. Various links between Fourier coefficients of Boolean functions and their complexity characteristics have been studied in a number of works, see [1, 2, 3, 4, 6, 8, 13, 19, 20, 22, 23]. In particular, these Institut fur Informatik, Technische Universitat Munchen, D 80290 Munchen, Germany. bernasco informatik.tu muenchen.de y Fachbereich fur Informatik, Universitat Trier, D 54286 Trier, Germany. damm uni trier.de z School of MPCE, Macquarie University, Sydney, NSW 2109, ....
.... have been obtained for Boolean functions deciding if a given integer is square free [5, 25] There are also some very interesting results about determinants [14, 15] In this paper we show that the spectral method for proving lower bounds on the size complexity of Boolean functions proposed in [1, 2] can be applied to functions related to some arithmetic properties of integers. The number theoretic counterpart of the spectral technique is a sieve method. Some preliminary results have been obtained in [5] We first consider the Boolean function g which decides whether a given (n 1) bit odd ....
[Article contains additional citation context not shown here]
A. Bernasconi, `On the complexity of balanced Boolean functions', Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 1203 (1997), 253-- 263.
Circuit Complexity of Testing Square-Free Numbers - Bernasconi, Shparlinski (1999) (1 citation) Self-citation (Bernasconi) (Correct)
....based on the Abstract Harmonic Analysis on the hypercube have been shown to represent a very useful tool for obtaining lower complexity bounds. Various links between Fourier 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. However, a limitation of such approach to the study of Boolean function complexity is that, besides the results for parity and threshold functions, spectral methods have ....
....extend the area of applications of the spectral techniques to the study of Boolean function complexity; ffi obtain the first non trivial lower bound on the circuit complexity of testing square free numbers. To this aim, we first provide a generalization of the spectral technique developed in [2, 3] for getting lower bounds on the size complexity of Boolean functions computed by constant depth circuits. We then apply the generalized technique to evaluate the complexity of the Boolean function which decides whether a given (n 1) bit odd integer is squarefree, that is the function for which ....
[Article contains additional citation context not shown here]
A. Bernasconi, `On the complexity of balanced Boolean functions', Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 1203 (1997), 253--263.
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