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We show that there is a randomized algorithm that, when given a small constant-depth Boolean circuit $C$ made up of gates that compute constant-degree Polynomial Threshold functions or PTFs (i.e., Boolean functions that compute signs of…
In pursuit of a deeper understanding of Boolean Promise Constraint Satisfaction Problems (PCSPs), we identify a class of problems with restricted structural complexity, which could serve as a promising candidate for complete…
We introduce the discrete version of the Hutchinson--Barnsley theory providing algorithms to approximate the Hutchinson measure for iterated function systems (IFS) and generalized iterated function systems (GIFS) complementing the discrete…
Nowadays genetic algorithm (GA) is greatly used in engineering pedagogy as an adaptive technique to learn and solve complex problems and issues. It is a meta-heuristic approach that is used to solve hybrid computation challenges. GA…
Recently Chen and Gao~\cite{ChenGao2017} proposed a new quantum algorithm for Boolean polynomial system solving, motivated by the cryptanalysis of some post-quantum cryptosystems. The key idea of their approach is to apply a Quantum Linear…
Let $g: \{-1,1\}^k \to \{-1,1\}$ be any Boolean function and $q_1,\dots,q_k$ be any degree-2 polynomials over $\{-1,1\}^n.$ We give a \emph{deterministic} algorithm which, given as input explicit descriptions of $g,q_1,\dots,q_k$ and an…
We consider positive solutions to parametrized systems of generalized polynomial equations (with real exponents and positive parameters). By a fundamental result obtained in parallel work, polynomial systems are determined by geometric…
We develop a pseudo-random generator to fool degree-$d$ polynomial threshold functions with respect to the Gaussian distribution. For $c>0$ any constant, we construct a pseudo-random generator that fools such functions to within $\epsilon$…
Feature selection is a problem of finding efficient features among all features in which the final feature set can improve accuracy and reduce complexity. In feature selection algorithms search strategies are key aspects. Since feature…
Representations of Boolean functions by real polynomials play an important role in complexity theory. Typically, one is interested in the least degree of a polynomial p(x_1,...,x_n) that approximates or sign-represents a given Boolean…
In this paper we study the complexity of quantum query algorithms computing the value of Boolean function and its relation to the degree of algebraic polynomial representing this function. We pay special attention to Boolean functions with…
Meta-heuristic techniques are important as they are used to find solutions to computationally intractable problems. Simplistic methods such as exhaustive search become computationally expensive and unreliable as the solution space for…
An improved characteristic set algorithm for solving Boolean polynomial systems is proposed. This algorithm is based on the idea of converting all the polynomials into monic ones by zero decomposition, and using additions to obtain…
We propose a framework of genetic algorithms which use multi-level hierarchies to solve an optimization problem by searching over the space of simpler objective functions. We solve a variant of Travelling Salesman Problem called…
A simple way to generate a Boolean function is to take the sign of a real polynomial in $n$ variables. Such Boolean functions are called polynomial threshold functions. How many low-degree polynomial threshold functions are there? The…
Coverage of image features play an important role in many vision algorithms since their distribution affect the estimated homography. This paper presents a Genetic Algorithm (GA) in order to select the optimal set of features yielding…
Genetic programming (GP) is a commonly used approach to solve symbolic regression (SR) problems. Compared with the machine learning or deep learning methods that depend on the pre-defined model and the training dataset for solving SR…
Query plans are compared according to multiple cost metrics in multi-objective query optimization. The goal is to find the set of Pareto plans realizing optimal cost tradeoffs for a given query. So far, only algorithms with exponential…
Generative semantic hashing is a promising technique for large-scale information retrieval thanks to its fast retrieval speed and small memory footprint. For the tractability of training, existing generative-hashing methods mostly assume a…
Genetic Algorithms (GAs) are explored as a tool for probing new physics with high dimensionality. We study the 19-dimensional pMSSM, including experimental constraints from all sources and assessing the consistency of potential signals of…