Related papers: Minsky machines and algorithmic problems
A short survey about combinatorics on words and algorithmic methods in a ring. Special attention is given to Shirshov's results. Adopted for undegraduate students.
We describe how orbital graphs can be used to improve the practical performance of many algorithms for permutation groups, including intersection and stabilizer problems. First we explain how orbital graphs can be integrated in partition…
The $k$-means algorithm is one of the most widely used clustering heuristics. Despite its simplicity, analyzing its running time and quality of approximation is surprisingly difficult and can lead to deep insights that can be used to…
Here we give a detailed proof for the crucial point in our Minsky machine simulation - that any linear logic derivation for a specific Horn sequent can be transformed into a Minsky computation leading from an initial configuration to the…
Minkowski sums are of theoretical interest and have applications in fields related to industrial backgrounds. In this paper we focus on the specific case of summing polytopes as we want to solve the tolerance analysis problem described in…
This article is partly a survey and partly a research paper. It tackles the use of Groebner bases for addressing problems of numerical semigroups, which is a topic that has been around for some years, but it does it in a systematic way…
As dynamic and control systems become more complex, relying purely on numerical computations for systems analysis and design might become extremely expensive or totally infeasible. Computer algebra can act as an enabler for analysis and…
The toric Hilbert scheme parametrizes all algebras isomorphic to a given semigroup algebra as a multigraded vectorspace. All components of the scheme are toric varieties, and among them, there is a fairly well understood coherent component.…
The survey presents the well-known Warshall's algorithm, a generalization and some interesting applications of this.
It has become trivial to point out how decision-making processes in various social, political and economical sphere are assisted by automated systems. Improved efficiency, the hallmark of these systems, drives the mass scale integration of…
Geometric semigroup theory is the systematic investigation of finitely-generated semigroups using the topology and geometry of their associated automata. In this article we show how a number of easily-defined expansions on finite semigroups…
The aim of these notes is to demonstrate the potential for ideas in machine learning to impact on the fields of inverse problems and data assimilation. The perspective is one that is primarily aimed at researchers from inverse problems…
This paper gives a brief overview of some new work in number theory and algebra, and also studies the arithmetic and algebraic properties of Minkowski balls and spheres. The content of the paper is presented in more detail in the table of…
Unfair metrical task systems are a generalization of online metrical task systems. In this paper we introduce new techniques to combine algorithms for unfair metrical task systems and apply these techniques to obtain improved randomized…
Mixed data comprises both numeric and categorical features, and mixed datasets occur frequently in many domains, such as health, finance, and marketing. Clustering is often applied to mixed datasets to find structures and to group similar…
When a semigroup has a unary operation, it is possible to define two binary operations, namely, left and right division. In addition it is well known that groups can be defined in terms of those two divisions. The aim of this paper is to…
In this paper, we systematically study generalized Markov numbers arising from semigroups of reduced integer matrices. This construction allows us to find these numbers by counting perfect matchings of a new family of bipartite graphs,…
For the first time, we have introduced the concept of N-groups, N-semigroups, N-loops, and N-groupoids. We also define a mixed N-algebraic structure. The main aim of this book is to attract young mathematicians to this interesting field. It…
Hilbert series are a standard tool in algebraic geometry, and more recently are finding many uses in theoretical physics. This summary reviews work applying machine learning to databases of them; and was prepared for the proceedings of the…
Optimization plays an important role in solving many inverse problems. Indeed, the task of inversion often either involves or is fully cast as a solution of an optimization problem. In this light, the mere non-linear, non-convex, and…