Related papers: Graph Field Automata
A cellular automata approach using a Directed Cyclic Graph is used to model interrelationships of fluctuating time, state and space. This model predicts phenomena including a constant and maximum speed at which any moving entity can travel,…
Graphings serve as limit objects for bounded-degree graphs. We define the ``cycle matroid'' of a graphing as a submodular setfunction, with values in [0,1], which generalizes (up to normalization) the cycle matroid of finite graphs. We…
In 2004, Klavins et al. introduced the use of graph grammars to describe -- and to program -- systems of self-assembly. It turns out that these graph grammars are a "dual notion" of a graph rewriting characterization of distributed systems…
In this thesis we present a semantic representation formalism based on directed graphs and explore its linguistic adequacy and explanatory benefits in the semantics of plurality and quantification. Our graph language covers the essentials…
This paper is devoted to present the Mathematics Grammar Library, a system for multilingual mathematical text processing. We explain the context in which it originated, its current design and functionality and the current development goals.…
We report on the automation of a technique to prove the correctness of program transformations in higher-order program calculi which may permit recursive let-bindings as they occur in functional programming languages. A program…
This is Chapter 24 in the "AutoMathA" handbook. Finite automata have been used effectively in recent years to define infinite groups. The two main lines of research have as their most representative objects the class of automatic groups…
Graphs play an important role in representing complex relationships in various domains like social networks, knowledge graphs, and molecular discovery. With the advent of deep learning, Graph Neural Networks (GNNs) have emerged as a…
Graph transformation formalisms have proven to be suitable tools for the modelling of chemical reactions. They are well established in theoretical studies and increasingly also in practical applications in chemistry. The latter is made…
The visualization of argumentation frameworks (AFs) is crucial for enabling a wide applicability of argumentative tools. However, their visualization is often considered only as an accompanying part of tools for computing semantics and…
Graphical (Linear) Algebra is a family of diagrammatic languages allowing to reason about different kinds of subsets of vector spaces compositionally. It has been used to model various application domains, from signal-flow graphs to Petri…
Automated Machine Learning (AutoML) has become increasingly popular in recent years due to its ability to reduce the amount of time and expertise required to design and develop machine learning systems. This is very important for the…
Researchers have relegated natural language processing tasks to Transformer-type models, particularly generative models, because these models exhibit high versatility when performing generation and classification tasks. As the size of these…
We overview dataflow matrix machines as a Turing complete generalization of recurrent neural networks and as a programming platform. We describe vector space of finite prefix trees with numerical leaves which allows us to combine expressive…
Automatic Text Summarization strategies have been successfully employed to digest text collections and extract its essential content. Usually, summaries are generated using textual corpora that belongs to the same domain area where the…
Recent e-graph applications have typically considered concrete semantics of expressions, where the notion of equivalence stems from concrete interpretation of expressions. However, equivalences that hold over one interpretation may not hold…
We investigate commutative images of languages recognised by register automata and grammars. Semi-linear and rational sets can be naturally extended to this setting by allowing for orbit-finite unions instead of only finite ones. We prove…
In the Matrix approach to graph transformation we represent simple digraphs and rules with Boolean matrices and vectors, and the rewriting is expressed using Boolean operations only. In previous works, we developed analysis techniques…
Data trees serve as an abstraction of structured data, such as XML documents. A number of specification formalisms for languages of data trees have been developed, many of them adhering to the paradigm of register automata, which is based…
Graphs are widely used as a popular representation of the network structure of connected data. Graph data can be found in a broad spectrum of application domains such as social systems, ecosystems, biological networks, knowledge graphs, and…