Related papers: An identification system based on the explicit iso…

In this paper, we present a simple bare-bones solution of a Zero-Knowledge authentication protocol which uses non-commutative algebra and a variation of the generalized symmetric decomposition problem (GSDP) as a one-way function. The…

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.

It is well-known that the graph isomorphism problem can be posed as an equivalent problem of determining whether an auxiliary graph structure contains a clique of specific order. However, the algorithms that have been developed so far for…

Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging…

This paper proposes a new algorithm for linear system identification from noisy measurements. The proposed algorithm balances a data fidelity term with a norm induced by the set of single pole filters. We pose a convex optimization problem…

Learning the unknown causal parameters of a linear structural causal model is a fundamental task in causal analysis. The task, known as the problem of identification, asks to estimate the parameters of the model from a combination of…

This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…

We present a constructive recognition algorithm to decide whether a given black-box group is isomorphic to an alternating or a symmetric group without prior knowledge of the degree. This eliminates the major gap in known algorithms, as they…

The isomorphism problem means to decide if two given finite-dimensional simple algebras over the same centre are isomorphic and, if so, to construct an isomorphism between them. A solution to this problem has applications in computational…

We live in an era of information and it is very important to handle the exchange of information. While sending data to an authorized source, we need to protect it from unauthorized sources, changes, and authentication. ZKP technique can be…

This paper introduces quantum analogues of non-interactive perfect and statistical zero-knowledge proof systems. Similar to the classical cases, it is shown that sharing randomness or entanglement is necessary for non-trivial protocols of…

The accurate identification of faulty hardware is a fundamental requirement for reliable quantum information processing. We address this problem in a quantum setting, where a series of $n$ devices is intended to apply the same unitary…

Binary classification is one of the most common problem in machine learning. It consists in predicting whether a given element belongs to a particular class. In this paper, a new algorithm for binary classification is proposed using a…

We propose a general way of constructing zero-knowledge authentication schemes from actions of a semigroup on a set, without exploiting any specific algebraic properties of the set acted upon. Then we give several concrete realizations of…

It is known that a graph isomorphism testing algorithm is polynomially equivalent to a detecting of a graph non-trivial automorphism algorithm. The polynomiality of the latter algorithm, is obtained by consideration of symmetry properties…

Graph isomorphism is an important computer science problem. The problem for the general case is unknown to be in polynomial time. The base algorithm for the general case works in quasi-polynomial time. The solutions in polynomial time for…

As it follows from G\"odel's incompleteness theorems, any consistent formal system of axioms and rules of inference should imply a true unprovable statement. Actually, this fundamental principle can be efficiently applicable in…

In the present work, a simple algorithm for stabilizing an unknown linear time-invariant system is proposed, assuming only that this system is stabilizable. The suggested algorithm is based on first performing a partial identification of…

Motivated by a certain molecular reconstruction methodology in cryo-electron microscopy, we consider the problem of solving a linear system with two unknown orthogonal matrices, which is a generalization of the well-known orthogonal…

We present an efficient computational representation of central simple algebras using Brauer factor sets. Using this representation and polynomial quantum algorithms for number theoretical tasks such as factoring and $S$-unit group…