Related papers: Minsky machines and algorithmic problems
Algebraic statistics is concerned with the study of probabilistic models and techniques for statistical inference using methods from algebra and geometry. This article presents a list of open mathematical problems in this emerging field,…
It is a survey of the main results on abstract characterizations of algebras of $n$-place functions obtained in the last 40 years. A special attention is paid to those algebras of $n$-place functions which are strongly connected with groups…
We give several algorithms addressing computations of intersections of conjugate subgroups.
Every semigroup which is a finite disjoint union of copies of the free mono- genic semigroup (natural numbers under addition) has soluble word prob- lem and soluble membership problem. Efficient algorithms are given for both problems.
In this paper we introduce a new algorithm to study some NP-complete problems. This algorithm is a Markov Chain Monte Carlo (MCMC) inspired by the cavity method developed in the study of spin glass. We will focus on the maximum clique…
One of the increasingly important technologies dealing with the growing complexity of the digitalization of almost all human activities is Artificial intelligence, more precisely machine learning Despite the fact, that we live in a Big data…
We study Smarandache sequences of numbers, and related problems, via a Computer Algebra System. Solutions are discovered, and some conjectures presented.
We introduce a novel technique to analyse unambiguous B\"uchi automata quantitatively, and apply this to the model checking problem. It is based on linear-algebra arguments that originate from the analysis of matrix semigroups with constant…
In this paper we further study properties of Magnus embedding, give a precise reducibility diagram for Dehn problems in groups of the form $F/N^{(d)}$, and provide a detailed answer to Problem 12.98 in Kourovka notebook. We also show that…
We overview some results on distributed learning with focus on a family of recently proposed algorithms known as non-Bayesian social learning. We consider different approaches to the distributed learning problem and its algorithmic…
In this paper, we provide an extensive overview of machine learning techniques applied to structural magnetic resonance imaging (MRI) data to obtain clinical classifiers. We specifically address practical problems commonly encountered in…
Biclustering, also called co-clustering, block clustering, or two-way clustering, involves the simultaneous clustering of both the rows and columns of a data matrix into distinct groups, such that the rows and columns within a group display…
In this review, we present some advanced algorithms and programs used in our scientific school with short description of types of astrophysical systems, which we study. However, we discuss mainly mathematical methods, which may be applied…
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…
This Ph.D. thesis contains original contributions to several areas within the disciplines of disordered systems, numerical linear algebra, and scientific computing: (1) Theoretical and numerical study of the errors caused by using certain…
A study of assisted problem solving formalized via decompositions of deterministic finite automata is initiated. The landscape of new types of decompositions of finite automata this study uncovered is presented. Languages with various…
We develop a full-fledged analysis of an algorithmic decision process that, in a multialternative choice problem, produces computable choice probabilities and expected decision times.
In this chapter we present transformation semigroups and their applications. We begin with Klein's approach to geometry based on invariants of transformation groups. Then we present symmetry groups in chemistry and in classical mechanics.…
Cylindrical algebraic decomposition(CAD) is a key tool in computational algebraic geometry, particularly for quantifier elimination over real-closed fields. When using CAD, there is often a choice for the ordering placed on the variables.…
This article is a survey of 0-cohomology of semigroups. The main attention is devoted to applications.