Scribe notes from the 2012 Barbados Workshop on Computational Complexity. A series of lectures on Analysis of Boolean Functions by Ryan O'Donnell, with a guest lecture by Per Austrin.

This paper addresses the question of making inferences regarding Boolean functions under conditions of (i) noise, or stochastic variation in observed data, and (ii) sparsity, by which we mean that the number of inputs or predictors far exceeds the arity of the underlying Boolean function. We put forward a simple probability model for such observations, and discuss model selection, parameter est...

This paper proposes analytical synthesis of the minimum L2-sensitivity realizations of all-pass digital filters. We first prove that the L2-sensitivity minimization problem can be solved analytically if the all second-order modes of a digital filter are equal. We focus on the fact that the second-order modes of all-pass digital filters are all unity. As a result, it is clarified that the minimu...

Classical learning algorithms for Boolean functions assume that unknown targets are Boolean functions over fixed variables. The assumption precludes scenarios where indefinitely many variables are needed. It also induces unnecessary queries when many variables are redundant. Based on a classical learning algorithm for Boolean functions, we develop two learning algorithms to infer Boolean functi...

Acknowledgments First of all I would like to thank Prof. Dr. Michael Hortmann for supervising this thesis. I am very grateful for him introducing me to cryptography and supporting me to attend Eurocrypt 2011 and Asiacrypt 2011. I am also very thankful for Prof. Dr. Gregor Leander who took the part of being my second supervisor. I am indebted to my fellow students for their camaraderie and encou...

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 spectr...

We consider the Fourier Entropy-Influence (FEI) conjecture in the context of cryptographic Boolean functions. We show that the FEI conjecture is true for the functions satisfying the strict avalanche criterion, which forms a subset of asymptotic log–density 1 in the set of all Boolean functions. Further, we prove that the FEI conjecture is satisfied for plateaued Boolean functions, monomial alg...