With cryptographic investigations, the design of Boolean functions is a wide area. The Boolean functions play important role in the construction of a symmetric cryptosystem. In this paper the modified hill climbing method is considered. The method allows using hill climbing techniques to modify bent functions used to design balanced, highly nonlinear Boolean functions with high algebraic degree...

The (fast) algebraic immunity, including (standard) algebraic immunity and the resistance against fast algebraic attacks, has been considered as an important cryptographic property for Boolean functions used in stream ciphers. This paper is on the determination of the (fast) algebraic immunity of a special class of Boolean functions, called Boolean power functions. An n-variable Boolean power f...

The decision tree complexity of a boolean function F of n arguments is the depth of a minimum-depth decision tree that computes F correctly on every input. A boolean function F of n arguments is cn-evasive if its decision tree complexity is cn, (c < 1). F is completely evasive, (n-evasive), if all of its arguments need to be probed in the worst case. When we restrict the properties and form of ...

K. Y. Sill Information Systems Laboratory Stanford University Stanford, CA, 94305 T. Kailath Informat.ion Systems Laboratory Stanford U ni versity Stanford, CA, 94305 '~le introduce a geometric approach for investigating the power of threshold circuits. Viewing n-variable boolean functions as vectors in 'R'2", we invoke tools from linear algebra and linear programming to derive new results on t...

The minimum number of NOT gates in a logic circuit computing a Boolean function is called the inversion complexity of the function. In 1957, A. A. Markov determined the inversion complexity of every Boolean function and proved that ⌈log 2 (d(f)+ 1)⌉ NOT gates are necessary and sufficient to compute any Boolean function f (where d(f) is the maximum number of value changes from greater to smaller...

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 ...