Related papers: Strong shift equivalence as a category notion
Category theory is a branch of mathematics that provides a formal framework for understanding the relationship between mathematical structures. To this end, a category not only incorporates the data of the desired objects, but also…
Significant pattern mining, the problem of finding itemsets that are significantly enriched in one class of objects, is statistically challenging, as the large space of candidate patterns leads to an enormous multiple testing problem.…
We introduce proof terms for string rewrite systems and, using these, show that various notions of equivalence on reductions known from the literature can be viewed as different perspectives on the notion of causal equivalence. In…
The thesis is devoted to relations between algebra and symbolic dynamics. Various generalisations of sturmian sequences are discoursed. Let $W$ be an infinite word over a finite alphabet $A$. The combinatorial criteria of existence of…
A $D_{\infty}$-topological Markov chain can be represented by a pair of zero-one square matrices, which is called a flip pair. We introduce the concepts of $D_{\infty}$-strong shift equivalence and $D_{\infty}$-shift equivalence, which are…
Ambiguity is shown in the context of the differential calculus of several variables and with the help of the language of category theory, a way to solve it in its most general form is offered. It is also shown that this new definition is…
This work describes the way that topological mixing and chaos in continua, as induced by discrete dynamical systems, can or can't be understood through topological conjugacy with symbolic dynamical systems. For example, there is no symbolic…
Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…
We present the notions of positively complete theory and general forms of amalgamation in the framework of positive logic. We explore the fundamental properties of positively complete theories and study the behaviour of companion theories…
Lada introduced strong homotopy algebras to describe the structures on a deformation retract of an algebra in topological spaces. However, there is no satisfactory general definition of a morphism of strong homotopy (s.h.) algebras. Given a…
The article addresses the problem whether indefinite double sums involving a generic sequence can be simplified in terms of indefinite single sums. Depending on the structure of the double sum, the proposed summation machinery may provide…
In this survey article we give a brief history of symbolic powers and its connection with the interesting problem of set-theoretic complete intersection. We also state a few problems and conjectures. Recently, in connection to symbolic…
Transductions are binary relations of finite words. For rational transductions, i.e., transductions defined by finite transducers, the inclusion, equivalence and sequential uniformisation problems are known to be undecidable. In this paper,…
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
This paper addresses the problem of checking invariant properties for a large class of symbolic transition systems, defined by a combination of SMT theories and quantifiers. State variables can be functions from an uninterpreted sort…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
We give a precise definition of ``generic-case complexity'' and show that for a very large class of finitely generated groups the classical decision problems of group theory - the word, conjugacy and membership problems - all have…
The unprecedented pace of machine learning research has lead to incredible advances, but also poses hard challenges. At present, the field lacks strong theoretical underpinnings, and many important achievements stem from ad hoc design…
We address the problem of defining graph transformations by the simultaneous application of direct transformations even when these cannot be applied independently of each other. An algebraic approach is adopted, with production rules of the…
In the theory of renormalization for classical dynamical systems, e.g. unimodal maps and critical circle maps, topological conjugacy classes are stable manifolds of renormalization. Physically more realistic systems on the other hand may…