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Abstract: In this paper, we study various combinatorial complexity characteristics of Boolean functions related to some natural arithmetic problems about polynomials over IF 2 . In particular, we consider the Boolean function deciding whether a given polynomial over IF 2 is squarefree. We obtain an exponential lower bound on the size of a decision tree for this function, and derive an asymptotic formula, having a linear main term, for its average sensitivity. This allows us to estimate other complexity... (Update)
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BibTeX entry: (Update)
@misc{ allender-complexity,
author = "Eric Allender and Anna Bernasconi and Carsten Damm and et al.",
title = "On the Complexity of Some Arithmetic Problems over F2[T]",
url = "citeseer.ist.psu.edu/442335.html" }
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10 Circuit complexity of testing square-free numbers - Bernasconi, Shparlinski - 1999
9 On polynomial representations of Boolean functions related t.. - Plaku, Shparlinski - 2001
9 Circuit and decision tree complexity of some number theoreti.. - Bernasconi, Damm et al.
8 Feasible timeoptimal algorithms for Boolean functions on exc.. - Dietzfelbinger, Kutylowski et al. - 1996
7 the average sensitivity of testing square-free numbers - Bernasconi, Damm et al. - 1999
5 A lower bound for primality - Allender, Saks et al. - 2001
5 the Fourier analysis of Boolean functions - Bernasconi, Codenotti et al. - 1996
4 Combinatorial properties of classes of functions hard to com.. (context) - Bernasconi - 1998
4 the complexity of balanced Boolean functions (context) - Bernasconi - 1999
2 The average sensitivity of square-freeness (context) - Bernasconi, Damm et al. - 2000
1 On P versus NP # co-NP for decision trees and read-once bran.. (context) - Jukna, Razborov et al. - 1999
1 1 1 formulae on finite structures (context) - Ajtai - 1983
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