Related papers: A One-Way Function Based On The Extended Euclidean…
We propose an algorithm for solving of the graph isomorphism problem. Also, we introduce the new class of graphs for which the graph isomorphism problem can be solved polynomially using the algorithm.
The problem of implementing a class of functions with particular conditions by using monotonic multilayer functions is considered. A genetic algorithm is used to create monotonic functions of a certain class, and these are implemented with…
In this paper, we consider the existence of a factorization of a monic, bounded motion polynomial. We prove existence of factorizations, possibly after multiplication with a real polynomial and provide algorithms for computing polynomial…
The existence of one-way functions is arguably the most important problem in computer theory. The article discusses and refines a number of concepts relevant to this problem. For instance, it gives the first combinatorial complete owf,…
Sigmoid functions play an important role in many areas of applied mathematics, including machine learning, population dynamics and probability. We place the study of sigmoid functions in the context of the derivative sub-group of the group…
Let $\mathrm{R}$ be a real closed field and $\mathrm{D} \subset \mathrm{R}$ an ordered domain. We consider the algorithmic problem of computing the generalized Euler-Poincar\'e characteristic of real algebraic as well as semi-algebraic…
Additive Fourier Transform is sdudied. A fast multiplication algorithm for polynomials over the binary field is given. The bit complexity of the algorithm is $O(n(log n)(\log\log n)^2)$.
The polynomial algebra is a deformed SU(2) algebra. Here, we use polynomial algebra as a method to solve a series of deformed oscillators. Meanwhile, we find a series of physics systems corresponding with polynomial algebra with different…
In this note we prove an explicit binomial formula for Jack polynomials and discuss some applications of it.
The so-called polynomial equations play an important role both in algebra and in the theory of functional equations. If the unknown functions in the equation are additive, relatively many results are known. However, even in this case, there…
We give a fast, exact algorithm for solving Dirichlet problems with polynomial boundary functions on quadratic surfaces in R^n such as ellipsoids, elliptic cylinders, and paraboloids. To produce this algorithm, first we show that every…
This paper presents the concept of digit polynomials, which leads to a deterministic and unconditional integer factorization algorithm with the runtime complexity $\mathcal{O}(N^{1/4+\epsilon})$. Strassen's well known factoring approach is…
We apply general difference calculus in order to obtain solutions to the functional equations of the second order. We show that factorization method can be successfully applied to the functional case. This method is equivariant under the…
Motion polynomials are a specific type of polynomial over a Clifford algebra that can conveniently describe rational motions. There exists an algorithm for the factorization of motion polynomials that works in generic cases. It hinges on…
A unifying scheme of classical special functions of hypergeometric type obeying orthogonality or biorthogonality relations is described. It expands the Askey scheme of classical orthogonal polynomials and its $q$-analogue based on the…
The determination of the computational complexity of multi-agent pathfinding on directed graphs has been an open problem for many years. For undirected graphs, solvability can be decided in polynomial time, as has been shown already in the…
A sharp bound is obtained for the number of ways to express the monomial $X^n$ as a product of linear factors over $\mathbb{Z}/p^{\alpha}\mathbb{Z}$. The proof relies on an induction-on-scale procedure which is used to estimate the number…
We use recent results on algorithms for Markov decision problems to show that a canonical form for a generalized P-matrix can be computed, in some important cases, by a strongly polynomial algorithm.
For odd square-free n > 1 the n-th cyclotomic polynomial satisfies an identity of Gauss. There are similar identity of Aurifeuille, Le Lasseur and Lucas. These identities all involve certain polynomials with integer coefficients. We show…
We consider optimization problems on manifolds with equality and inequality constraints. A large body of work treats constrained optimization in Euclidean spaces. In this work, we consider extensions of existing algorithms from the…