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Query rewrite systems perform graph substitutions using rewrite rules to generate optimal SQL query plans. Rewriting logical and physical relational query plans is proven to be an NP-hard sequential decision-making problem with a search…
We study the synchronous and asynchronous automatic structures on the fundamental group of a graph of groups in which each edge group is finite. Up to a natural equivalence relation, the set of biautomatic structures on such a graph product…
Graph Interpolation Grammars are a declarative formalism with an operational semantics. Their goal is to emulate salient features of the human parser, and notably incrementality. The parsing process defined by GIGs incrementally builds a…
Graph-based Retrieval-Augmented Generation (Graph-RAG) enhances large language models (LLMs) by structuring retrieval over an external corpus. However, existing approaches typically assume a static corpus, requiring expensive full-graph…
Graph data structures offer a versatile and powerful means to model relationships and interconnections in various domains, promising substantial advantages in data representation, analysis, and visualization. In games, graph-based data…
This paper introduces Graph Convolutional Recurrent Network (GCRN), a deep learning model able to predict structured sequences of data. Precisely, GCRN is a generalization of classical recurrent neural networks (RNN) to data structured by…
Datasets from several domains, such as life-sciences, semantic web, machine learning, natural language processing, etc. are naturally structured as acyclic graphs. These datasets, particularly those in bio-informatics and computational…
General treebank analyses are graph structured, but parsers are typically restricted to tree structures for efficiency and modeling reasons. We propose a new representation and algorithm for a class of graph structures that is flexible…
We propose a modal logic tailored to describe graph transformations and discuss some of its properties. We focus on a particular class of graphs called termgraphs. They are first-order terms augmented with sharing and cycles. Termgraphs…
Cellular automata are discrete and computational models thatcan be shown as general models of complexity. They are used in varied applications to derive the generalized behavior of the presented model. In this paper we have took one such…
Hierarchical structure and repetition are prevalent in graphs originating from nature or engineering. These patterns can be represented by a class of parametric-structure graphs, which are defined by templates that generate structure by way…
Graph-structured data appears frequently in domains including chemistry, natural language semantics, social networks, and knowledge bases. In this work, we study feature learning techniques for graph-structured inputs. Our starting point is…
Graph transformation systems have the potential to be realistic models of chemistry, provided a comprehensive collection of reaction rules can be extracted from the body of chemical knowledge. A first key step for rule learning is the…
In structural proof theory, designing and working on large calculi make it difficult to get intuitions about each rule individually and as part of a whole system. We introduce two novel tools to help working on calculi using the approach of…
Architectural Design Rewriting (ADR, for short) is a rule-based formal framework for modelling the evolution of architectures of distributed systems. Rules allow ADR graphs to be refined. After equipping ADR with a simple logic, we equip…
Retrieval-augmented generation (RAG) empowers large language models to access external and private corpus, enabling factually consistent responses in specific domains. By exploiting the inherent structure of the corpus, graph-based RAG…
This book objective is to develop an algebraization of graph grammars. Equivalently, we study graph dynamics. From the point of view of a computer scientist, graph grammars are a natural generalization of Chomsky grammars for which a purely…
A theory is developed which uses "networks" (directed acyclic graphs with some extra structure) as a formalism for expressions in multilinear algebra. It is shown that this formalism is valid for arbitrary PROPs (short for 'PROducts and…
We study self-similarity in one-dimensional probabilistic cellular automata (PCA) using the renormalization technique. We introduce a general framework for algebraic construction of renormalization groups (RG) on cellular automata and apply…
We present the spectrum of the (normalized) graph Laplacian as a systematic tool for the investigation of networks, and we describe basic properties of eigenvalues and eigenfunctions. Processes of graph formation like motif joining or…