Related papers: Matrix Graph Grammars
I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…
Neural networks that compute over graph structures are a natural fit for problems in a variety of domains, including natural language (parse trees) and cheminformatics (molecular graphs). However, since the computation graph has a different…
The literature on word-representable graphs is quite rich, and a number of variations of the original definition have been proposed over the years. We are initiating a systematic study of such variations based on formal languages. In our…
One of the principal goals of graph modeling is to capture the building blocks of network data in order to study various physical and natural phenomena. Recent work at the intersection of formal language theory and graph theory has explored…
Indexed languages are interesting in computational linguistics because they are the least class of languages in the Chomsky hierarchy that has not been shown not to be adequate to describe the string set of natural language sentences. We…
We consider a core language of graph queries. These queries are seen as formulas to be solved with respect to graph-oriented databases. For this purpose, we first define a graph query algebra where some operations over graphs and sets of…
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…
The analysis of graphs has become increasingly important to a wide range of applications. Graph analysis presents a number of unique challenges in the areas of (1) software complexity, (2) data complexity, (3) security, (4) mathematical…
Large language models (LLMs) have recently taken the world by storm. They can generate coherent text, hold meaningful conversations, and be taught concepts and basic sets of instructions - such as the steps of an algorithm. In this context,…
Graphs are fundamental mathematical structures used in various fields to represent data, signals and processes. In this paper, we propose a novel framework for learning/estimating graphs from data. The proposed framework includes (i)…
Recent work at the intersection of formal language theory and graph theory has explored graph grammars for graph modeling. However, existing models and formalisms can only operate on homogeneous (i.e., untyped or unattributed) graphs. We…
Graphs are central to the chemical sciences, providing a natural language to describe molecules, proteins, reactions, and industrial processes. They capture interactions and structures that underpin materials, biology, and medicine. This…
Graph transformations definable in logic can be described using the notion of transductions. By understanding transductions as a basic embedding mechanism, which captures the possibility of encoding one graph in another graph by means of…
The ability to read, write, and speak mathematics is critical to students becoming comfortable with statistical models and skills. Faster development of those skills may act as encouragement to further engage with the discipline. Vocabulary…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
A perspective of statistical language models which emphasizes their collocational aspect is advocated. It is suggested that strings be generalized in terms of classes of relationships instead of classes of objects. The single most important…
Graph grammars extend the theory of formal languages in order to model distributed parallelism in theoretical computer science. We show here that to certain classes of context-free and context-sensitive graph grammars one can associate a…
Formal grammars are extensively used in Computer Science and related fields to study the rules which govern production of a language. The use of these grammars can be extended beyond mere language production. One possibility is to view…
Grammar-based compression is a widely-accepted model of string compression that allows for efficient and direct manipulations on the compressed data. Most, if not all, such manipulations rely on the primitive \emph{random access} queries, a…
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…