Related papers: On Languages Describing Large Graph Classes
The class of Parikh word representable graphs were recently introduced. In this work, we further develop its general theory beyond the binary alphabet. Our main result shows that this class is equivalent to the class of bipartite…
This report is a survey of the relationships between various state-of-the-art neural network architectures and formal languages as, for example, structured by the Chomsky Language Hierarchy. Of particular interest are the abilities of a…
Many problems, especially those with a composite structure, can naturally be expressed in higher order logic. From a KR perspective modeling these problems in an intuitive way is a challenging task. In this paper we study the graph mining…
With the advent of end-to-end deep learning approaches in machine translation, interest in word alignments initially decreased; however, they have again become a focus of research more recently. Alignments are useful for typological…
Large Language Models (LLMs) have achieved impressive results in processing text data, which has sparked interest in applying these models beyond textual data, such as graphs. In the field of graph learning, there is a growing interest in…
Traditionally, graph algorithms get a single graph as input, and then they should decide if this graph satisfies a certain property $\Phi$. What happens if this question is modified in a way that we get a possibly infinite family of graphs…
Distinct letters $x$ and $y$ alternate in a word $w$ if after deleting in $w$ all letters but the copies of $x$ and $y$ we either obtain a word of the form $xyxy\cdots$ (of even or odd length) or a word of the form $yxyx\cdots$ (of even or…
As a supplement to my talk at the workshop, this extended abstract motivates and summarizes my work with co-authors on problems in two separate areas: first, in the lambda-calculus with letrec, a universal model of computation, and second,…
A graph $G = (V,E)$ is word-representable if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $w$ if and only if $xy$ is an edge in $E$. Word-representable graphs are the subject of a long research…
Graph learning is a prevalent domain that endeavors to learn the intricate relationships among nodes and the topological structure of graphs. Over the years, graph learning has transcended from graph theory to graph data mining. With the…
We present a framework for representing and modeling data on graphs. Based on this framework, we study three typical classes of graph signals: smooth graph signals, piecewise-constant graph signals, and piecewise-smooth graph signals. For…
After a period of decrease, interest in word alignments is increasing again for their usefulness in domains such as typological research, cross-lingual annotation projection, and machine translation. Generally, alignment algorithms only use…
In this paper, we discuss a method for identifying a seed word that would best represent a class of named entities in a graphical representation of words and their similarities. Word networks, or word graphs, are representations of…
We propose a concrete surface representation of abstract categorial grammars in the category of word cobordisms or cowordisms for short, which are certain bipartite graphs decorated with words in a given alphabet, generalizing linear logic…
A graph $G=(V,E)$ is word-representable if and only if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$, $x\neq y$, alternate in $w$ if and only if $xy\in E$. A split graph is a graph in which the vertices can be…
A graph $G=(V,E)$ is word-representable if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $w$ if and only if $(x,y)$ is an edge in $E$. A graph is word-representable if and only if it is…
We model and compute the probability distribution of the letters in random generated words in a language by using the theory of set partitions, Young tableaux and graph theoretical representation methods. This has been of interest for…
Large language models (LLMs) such as GPT-4 have emerged as frontrunners, showcasing unparalleled prowess in diverse applications, including answering queries, code generation, and more. Parallelly, graph-structured data, an intrinsic data…
Formal languages are sets of strings of symbols described by a set of rules specific to them. In this note, we discuss a certain class of formal languages, called regular languages, and put forward some elementary results. The properties of…
The study of graph queries in database theory has spanned more than three decades, resulting in a multitude of proposals for graph query languages. These languages differ in the mechanisms. We can identify three main families of languages,…