Related papers: Drag Rewriting
The representation of graphs is commonly based on the adjacency matrix concept. This formulation is the foundation of most algebraic and computational approaches to graph processing. The advent of deep learning language models offers a wide…
Rewriting is a common approach to logic optimization based on local transformations. Most commercially available logic synthesis tools include a rewriting engine that may be used multiple times on the same netlist during optimization. This…
We present a new graph compressor that works by recursively detecting repeated substructures and representing them through grammar rules. We show that for a large number of graphs the compressor obtains smaller representations than other…
In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…
Graph transformation is the rule-based modification of graphs, and is a discipline dating back to the 1970s. The declarative nature of graph rewriting rules comes at a cost. In general, to match the left-hand graph of a fixed rule within a…
In this paper, we propose a new type of graph, denoted as "embedded-graph", and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated…
We study the relation between algebraic structures and Graph Theory. We have defined five different weighted digraphs associated to a finite dimensional algebra over a field in order to tackle important properties of the associated…
Nowadays, Web Services (WS) remain a main actor in the implementation of distributed applications. They represent a new promising paradigm for the development, deployment and integration of Internet applications. These services are in most…
String diagrams are pictorial representations for morphisms of symmetric monoidal categories. They constitute an intuitive and expressive graphical syntax, which has found application in a very diverse range of fields including concurrency…
Graph is a useful data structure to model various real life aspects like email communications, co-authorship among researchers, interactions among chemical compounds, and so on. Supporting such real life interactions produce a knowledge…
We generalize the problem of reconstructing strings from their substring compositions first introduced by Acharya et al. in 2015 motivated by polymer-based advanced data storage systems utilizing mass spectrometry. Namely, we see strings as…
Order diagrams allow human analysts to understand and analyze structural properties of ordered data. While an experienced expert can create easily readable order diagrams, the automatic generation of those remains a hard task. In this work,…
The degree sequence of a graph is a numerical method to characterize the properties of graphs. Generalized forms of degree sequences exist for complete graphs and complete graphs. Nikolopolus et al. characterized the number of spanning…
This paper presents general syntactic conditions ensuring the strong normalization and the logical consistency of the Calculus of Algebraic Constructions, an extension of the Calculus of Constructions with functions and predicates defined…
It has long been known that the combinatorial properties of a graph $\Gamma$ are closely related to the group theoretic properties of its right angled artin group (raag). It's natural to ask if the graph homomorphisms are similarly related…
Higher-dimensional rewriting is founded on a duality of rewrite systems and cell complexes, connecting computational mathematics to higher categories and homotopy theory: the two sides of a rewrite rule are two halves of the boundary of an…
In order to define graph transformations by the simultaneous application of concurrent rules, we have adopted in previous work a structure of attributed graphs stable by unions. We analyze the consequences on parallel independence, a…
We propose the use of hyperedge replacement graph grammars for factor graphs, or factor graph grammars (FGGs) for short. FGGs generate sets of factor graphs and can describe a more general class of models than plate notation, dynamic…
Large language models often encounter challenges with static knowledge and hallucinations, which undermine their reliability. Retrieval-augmented generation (RAG) mitigates these issues by incorporating external information. However, user…
We study directed random graphs (random graphs whose edges are directed), and present new results on the so-called strong components of those graphs. We provide analytic and simulation results on two special classes of strong component,…