Related papers: Nonlinearity of Boolean functions: an algorithmic …
In this paper we consider systems of partial (multidimensional) linear difference equations. Specifically, such systems arise in scientific computing under discretization of linear partial differential equations and in computational high…
A new algorithms for computing discrete logarithms on elliptic curves defined over finite fields is suggested. It is based on a new method to find zeroes of summation polynomials. In binary elliptic curves one is to solve a cubic system of…
In this note, we extend modular techniques for computing Gr\"obner bases from the commutative setting to the vast class of noncommutative $G$-algebras. As in the commutative case, an effective verification test is only known to us in the…
Nonlinear boolean equation systems play an important role in a wide range of applications. Grover's algorithm is one of the best-known quantum search algorithms in solving the nonlinear boolean equation system on quantum computers. In this…
Boolean functions can be represented in many ways including logical forms, truth tables, and polynomials. Additionally, Boolean functions have different canonical representations such as minimal disjunctive normal forms. Other canonical…
The lower and upper bound of any given algorithm is one of the most crucial pieces of information needed when evaluating the computational effectiveness for said algorithm. Here a novel method of Boolean Algebraic Programming for symbolic…
We consider the problem of optimizing a nonlinear objective function over a weighted independence system presented by a linear-optimization oracle. We provide a polynomial-time algorithm that determines an r-best solution for nonlinear…
We relate the computational complexity of finite strings to universal representations of their underlying symmetries. First, Boolean functions are classified using the universal covering topologies of the circuits which enumerate them. A…
Exhibiting an explicit Boolean function with a large high-order nonlinearity is an important problem in cryptography, coding theory, and computational complexity. We prove lower bounds on the second-order, third-order, and higher-order…
We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…
We consider some random series parametrised by complex binary strings. The simplest case is that of Rademacher series, independent of a time parameter. This is then extended to the case of Fourier series on the circle with Rademacher…
We study weak solutions to nonlocal equations governed by integrodifferential operators. Solutions are defined with the help of symmetric nonlocal bilinear forms. Throughout this work, our main emphasis is on operators with general,…
In this paper, we explore the merits of various algorithms for polynomial optimization problems, focusing on alternatives to sum of squares programming. While we refer to advantages and disadvantages of Quantifier Elimination, Reformulation…
Solving a polynomial system, or computing an associated Gr\"obner basis, has been a fundamental task in computational algebra. However, it is also known for its notorious doubly exponential time complexity in the number of variables in the…
We investigate the power of graph isomorphism algorithms based on algebraic reasoning techniques like Gr\"obner basis computation. The idea of these algorithms is to encode two graphs into a system of equations that are satisfiable if and…
For three decades binary decision diagrams, a data structure efficiently representing Boolean functions, have been widely used in many distinct contexts like model verification, machine learning, cryptography and also resolution of…
A wide array of graphical models can be parametrised to have atomic probabilities represented by monomial functions. Such monomial structure has proven very useful when studying robustness under the assumption of a multilinear model where…
In this paper we present an algorithm for construction of minimal involutive polynomial bases which are Groebner bases of the special form. The most general involutive algorithms are based on the concept of involutive monomial division…
This paper introduces a novel quantum algorithm that is able to classify a hierarchy of classes of imbalanced Boolean functions. The fundamental characteristic of imbalanced Boolean functions is that the proportion of elements in their…
Polynomial regression is a recurrent problem with a large number of applications. In computer vision it often appears in motion analysis. Whatever the application, standard methods for regression of polynomial models tend to deliver biased…