Wedetermine the complexity of evaluatingmonotone Boolean functions in a variant of the decision tree model introduced in [Charikar et al. 2002]. In thismodel, reading different variables can incur different costs, and competitive analysis is employed to evaluate the performance of the algorithms. It is known that for a monotone Boolean function f, the size of the largest certificate, aka PROOF ...

In this paper we simplify the definition of the weighted sum Boolean function which used to be inconvenient to compute and use. We show that the new function has essentially the same properties as the previous one. In particular, the bound on the average sensitivity of the weighted sum Boolean function remains unchanged after the simplification.

Boolean concepts are concepts whose membership is determined by a Boolean function, such as that expressed by a formula of propositional logic. Certain Boolean concepts have been much studied in the psychological literature, in particular with regard to their ease of learning. But research attention has been somewhat uneven, with a great deal of attention paid to certain concepts and little to ...

Let ǫ ∈ [0, 1/2] be the noise parameter and p > 1. We study the isoperimetric problem that for fixed mean Ef which Boolean function f maximizes the p-th moment E(Tǫf) p of the noise operator Tǫ acting on Boolean functions f : {0, 1} n 7→ {0, 1}. Our findings are: in the low noise scenario, i.e., ǫ is small, the maximum is achieved by the lexicographical function; in the high noise scenario, i.e...

Abstract. The equivalence of the characteristic function approach and the probabilistic approach to monotone and boolean convolutions is proven for non-compactly supported probability measures. A probabilistically motivated definition of the multiplicative boolean convolution of probability measures on the positive half-line is proposed. Unlike Bercovici’s multiplicative boolean convolution it ...

In this paper, we obtain a characterization of generalized Boolean functions based on spectral analysis. We investigate a relationship between the Walsh-Hadamard spectrum and σ f , the sum-of-squares-modulus indicator (SSMI) of the generalized Boolean function. It is demonstrated that σ f = 22n+s for every s-plateaued generalized Boolean function in n variables. Two classes of generalized semi-...

Usually, important parameters in the design and implementation of combinational logic circuits are the number of gates, transistors, and the levels used in the design of the circuit. In this regard, various evolutionary paradigms with different competency have recently been introduced. However, while being advantageous, evolutionary paradigms also have some limitations including: a) lack of con...

INTRODUCTION In an important class of stream ciphers, called combination generators, the key stream is produced by combining the outputs of several independent Linear Feedback Shift Register (LFSR) sequences with a nonlinear Boolean function. Siegenthaler [12] was the first to point out that the combining function should possess certain properties in order to resist divide-and-conquer attacks.A...

In view of the construction requirements of Boolean functions with many good cryptography properties, through the analysis of the relationship between the function values on the vectors with weight not more than d and the algebraic immunity, a method to determine the higher order algebraic immunity function is given. Meanwhile, a method that appropriate change in the function value without redu...

Card-based protocols that are based on a deck of physical cards achieve secure multi-party computation with information-theoretic secrecy. Using existing AND, XOR, NOT, and copy protocols, one can naively construct a secure computation protocol for any given (multivariable) Boolean function as long as there are plenty of additional cards. However, an explicit sufficient number of cards for comp...