相关论文: From Relation to Emulation and Interpretation: Com…
Constructing complex computation from simpler building blocks is a defining problem of computer science. In algebraic automata theory, we represent computing devices as semigroups. Accordingly, we use mathematical tools like products and…
Semigroup theory is a branch of abstract algebra, and it provides mathematical tools for the theory of computation. Finite semigroups can describe state transition systems and thus they model physically realizable computers. Engineering…
Programming languages tend to evolve over time to use more and more concepts from theoretical computer science. Still, there is a gap between programming and pure mathematics. Not all theoretical results have realized their promising…
We present an understandable, efficient, and streamlined proof of the Holonomy Decomposition for finite transformation semigroups and automata. This constructive proof closely follows the existing computational implementation. Its novelty…
Tasks like image reconstruction in computer vision, matrix completion in recommender systems and link prediction in graph theory, are well studied in machine learning literature. In this work, we apply a denoising autoencoder-based neural…
Graph kernels are kernel methods measuring graph similarity and serve as a standard tool for graph classification. However, the use of kernel methods for node classification, which is a related problem to graph representation learning, is…
Entanglement transformation of composite quantum systems is investigated in the context of group representation theory. Representation of the direct product group $SL(2,C)\otimes SL(2,C)$, composed of local operators acting on the binary…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
This paper describes an approach to computer aided calculations in the cohomology of arithmetic groups. It complements existing literature on the topic by emphasizing homotopies and perturbation techniques, rather than cellular subdivision,…
The residual finite-dimensionality of a $\mathrm{C}^*$-algebra is known to be encoded in a topological property of its space of representations, stating that finite-dimensional representations should be dense therein. We extend this…
The CREAM GAP package computes automorphisms, congruences, endomorphisms and subalgebras of algebras with an arbitrary number of binary and unary operations; it also decides if between two such algebras there exists a monomorphism, an…
A graph covering projection, also referred to as a locally bijective homomorphism, is a mapping between the vertices and edges of two graphs that preserves incidences and is a local bijection. This concept originates in topological graph…
Embedding-based methods for reasoning in knowledge hypergraphs learn a representation for each entity and relation. Current methods do not capture the procedural rules underlying the relations in the graph. We propose a simple…
The structure of transformation semigroups on a finite set is analyzed by introducing a hierarchy of functions mapping subsets to subsets. The resulting hierarchy of semigroups has a corresponding hierarchy of minimal ideals, or kernels.…
Steinberg's tensor product theorem shows that for semisimple algebraic groups the study of irreducible representations of higher Frobenius kernels reduces to the study of irreducible representations of the first Frobenius kernel. In the…
We investigate a semigroup construction related to the two-sided wreath product. It encompasses a range of known constructions and gives a slightly finer version of the decomposition in the Krohn-Rhodes Theorem, in which the three-element…
In this paper, we introduce a new image representation based on a multilayer kernel machine. Unlike traditional kernel methods where data representation is decoupled from the prediction task, we learn how to shape the kernel with…
This paper provides short proofs of two fundamental theorems of finite semigroup theory whose previous proofs were significantly longer, namely the two-sided Krohn-Rhodes decomposition theorem and Henckell's aperiodic pointlike theorem,…
We investigate a semigroup construction generalising the two-sided wreath product. We develop the foundations of this construction and show that for groups it is isomorphic to the usual wreath product. We also show that it gives a slightly…
We study the kernels of representations of mapping class groups of surfaces on twisted homologies of configuration spaces. We relate them with the kernel of a natural twisted intersection pairing: if the latter kernel is trivial then the…