information retrieval can be achieved through computerized processes by generating a list of relevant responses to a query. the document processor, matching function and query analyzer are the main components of an information retrieval system. document retrieval system is fundamentally based on: boolean, vector-space, probabilistic, and language models. in this paper, a new methodology for mat...

Here, we give a complete description of the entire c-Boomerang Connectivity Table for Gold function over finite fields even characteristic, by using double Weil sums. As by-product, generalize result Boura and Canteaut (IACR Trans. Symmetric Cryptol. 2018(3) : 290–310, 2018) classical boomerang uniformity (see also extended abstract Eddahmani Mesnager at Boolean Functions their Applications (BF...

In this lecture, we will first consider the problem of boolean function evaluation and prove that randomized algorithms (in the expected case) perform better than deterministic algorithms. The boolean circuits that we consider, can be naturally extended to obtain a game tree. We will then state Von Neumann’s minimax theorem and its extension Yao’s principle. Finally, we show how Yao’s principle...

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...

by the method of weight coefficients, techniques of real analysis andhermite-hadamard's inequality, a half-discrete hardy-hilbert-type inequalityrelated to the kernel of the hyperbolic cosecant function with the best possibleconstant factor expressed in terms of the extended riemann-zeta function is proved.the more accurate equivalent forms, the operator expressions with the norm,the reverses a...

We define an infinite class of 2-pile subtraction games, where the amount that can be subtracted from both piles simultaneously is an extended Boolean function f of the size of the piles, or a function over GF(2). Wythoff’s game is a special case. For each game, the 2nd player winning positions are a pair of complementary sequences. Sample games are presented, strategy complexity questions are ...

Causal independence modelling is a well-known method both for reducing the size of probability tables and for explaining the underlying mechanisms in Bayesian networks. In this paper, we propose an application of an extended class of causal independence models, causal independence models based on the symmetric Boolean function, for classification. We present an EM algorithm to learn the paramet...

We show that Nechiporuk’s method [14] for proving lower bound for Boolean formulas can be extended to the quantum case. This leads to an Ω(n2/ log n) lower bound for quantum formulas computing an explicit function. The only known previous explicit lower bound for quantum formulas [15] states that the majority function does not have a linear–size quantum formula.