Related papers: Specifying Graph Languages with Type Graphs

In modern mathematics, graphs figure as one of the better-investigated class of mathematical objects. Various properties of graphs, as well as graph-processing algorithms, can be useful if graphs of a certain kind are used as denotations…

We introduce regular languages of morphisms in free monoidal categories, with their associated grammars and automata. These subsume the classical theory of regular languages of words and trees, but also open up a much wider class of…

A split graph is a graph whose vertex set can be partitioned into a clique and an independent set. The word-representability of split graphs was studied in a series of papers in the literature, and the class of word-representable split…

Graph convexity has been used as an important tool to better understand the structure of classes of graphs. Many studies are devoted to determine if a graph equipped with a convexity is a {\em convex geometry}. In this work we survey…

We introduce type annotations as a flexible typing mechanism for graph systems and discuss their advantages with respect to classical typing based on graph morphisms. In this approach the type system is incorporated with the graph and…

Signed graphs are an emergent way of representing data in a variety of contexts where antagonistic interactions exist. These include data from biological, ecological, and social systems. Here we propose the concept of communicability for…

Large language models (LLMs) are increasingly adopted for a variety of tasks with implicit graphical structures, such as planning in robotics, multi-hop question answering or knowledge probing, structured commonsense reasoning, and more.…

In a recent work, we introduced a parametric framework for obtaining obstruction characterizations of graph parameters with respect to a quasi-ordering $\leqslant$ on graphs. Towards this, we proposed the concepts of class obstruction,…

Graphs are a powerful tool for representing and analyzing complex relationships in real-world applications such as social networks, recommender systems, and computational finance. Reasoning on graphs is essential for drawing inferences…

Graph mining is an important area in data mining and machine learning that involves extracting valuable information from graph-structured data. In recent years, significant progress has been made in this field through the development of…

We study topological properties of the graph topology.

Graphs that are squares under the gluing algebra arise in the study of homomorphism density inequalities such as Sidorenko's conjecture. Recent work has focused on these homomorphism density applications. This paper takes a new perspective…

A biform theory is a combination of an axiomatic theory and an algorithmic theory that supports the integration of reasoning and computation. These are ideal for formalizing algorithms that manipulate mathematical expressions. A theory…

Causal reasoning is a cornerstone of how humans interpret the world. To model and reason about causality, causal graphs offer a concise yet effective solution. Given the impressive advancements in language models, a crucial question arises:…

Regular word grammars are restricted context-free grammars that define all the recognizable languages of words. This paper generalizes regular grammars from words to certain classes of graphs, by defining regular grammars for unordered…

In many ways, graphs are the main modality of data we receive from nature. This is due to the fact that most of the patterns we see, both in natural and artificial systems, are elegantly representable using the language of graph structures.…

We show that the directed labelled Cayley graphs coincide with the rooted deterministic vertex-transitive simple graphs. The Cayley graphs are also the strongly connected deterministic simple graphs of which all vertices have the same cycle…

In fields ranging from business to systems biology, directed graphs with edges labeled by signs are used to model systems in a simple way: the nodes represent entities of some sort, and an edge indicates that one entity directly affects…

A fundamental question in natural language processing is - what kind of language structure and semantics is the language model capturing? Graph formats such as knowledge graphs are easy to evaluate as they explicitly express language…

We investigate some basic questions about the interaction of regular and rational relations on words. The primary motivation comes from the study of logics for querying graph topology, which have recently found numerous applications. Such…