Related papers: Homomorphisms on graph-walking automata
In this paper, inspired by the elegant work of Good and Meddaugh \cite{GM} and the graph models for zero-dimensional systems developed by several authors, like Gambaudo and Martens \cite{GM06}, Shimomura \cite{Sh14}. We try to discover a…
We describe an algorithm that morphs between two planar orthogonal drawings $\Gamma_I$ and $\Gamma_O$ of a connected graph $G$, while preserving planarity and orthogonality. Necessarily $\Gamma_I$ and $\Gamma_O$ share the same combinatorial…
The graph identification problem consists of discovering the interactions among nodes in a network given their state/feature trajectories. This problem is challenging because the behavior of a node is coupled to all the other nodes by the…
Recent years have witnessed significant advancements in machine learning methods on graphs. However, transferring knowledge effectively from one graph to another remains a critical challenge. This highlights the need for algorithms capable…
Automata networks can be seen as bare finite dynamical systems, but their growing theory has shown the importance of the underlying communication graph of such networks. This paper tackles the question of what dynamics can be realized up to…
Linearly bounded Turing machines have been mainly studied as acceptors for context-sensitive languages. We define a natural class of infinite automata representing their observable computational behavior, called linearly bounded graphs.…
We initiate the study of what we refer to as random walk labelings of graphs. These are graph labelings that are obtainable by performing a random walk on the graph, such that the labeling occurs increasingly whenever an unlabeled vertex is…
If $f : \tilde{\Gamma} \rightarrow \Gamma$ is a covering map between connected graphs, and $H$ is the subgroup of $\pi_1(\Gamma,v)$ used to construct the cover, then it is well known that the group of deck transformations of the cover is…
Quantum random walks have been shown to be powerful quantum algorithms for certain tasks on graphs like database searching, quantum simulations etc. In this work we focus on its applications for the graph isomorphism problem. In particular…
Graph Neural Networks (GNNs) excel at analyzing graph-structured data but struggle on heterophilic graphs, where connected nodes often belong to different classes. While this challenge is commonly addressed with specialized GNN…
Graphs (networks) are ubiquitous and allow us to model entities (nodes) and the dependencies (edges) between them. Learning a useful feature representation from graph data lies at the heart and success of many machine learning tasks such as…
We investigate families of infinite automata for context-sensitive languages. An infinite automaton is an infinite labeled graph with two sets of initial and final vertices. Its language is the set of all words labelling a path from an…
We introduce (weak) oddomorphisms of graphs which are homomorphisms with additional constraints based on parity. These maps turn out to have interesting properties (e.g., they preserve planarity), particularly in relation to homomorphism…
Transformers have become a central architecture for graph learning, but their application to graphs requires first choosing a tokenization: a graph-to-token map that determines which structural information is exposed at the input. In this…
Counting homomorphisms from a graph $H$ into another graph $G$ is a fundamental problem of (parameterized) counting complexity theory. In this work, we study the case where \emph{both} graphs $H$ and $G$ stem from given classes of graphs:…
We consider two random walks evolving synchronously on a random out-regular graph of $n$ vertices with bounded out-degree $r\ge 2$, also known as a random Deterministic Finite Automaton (DFA). We show that, with high probability with…
Word-representable graphs, which are the same as semi-transitively orientable graphs, generalize several fundamental classes of graphs. In this paper we propose a novel approach to study word-representability of graphs using a technique of…
We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…
Graph neural networks (GNNs) are commonly described as being permutation equivariant with respect to node relabeling in the graph. This symmetry of GNNs is often compared to the translation equivariance of Euclidean convolution neural…
Path graphs are intersection graphs of paths in a tree.~In this paper we give a "6\ good characterization" of path graphs, namely, we prove that path graph membership is in $NP\cap CoNP$ without resorting to existing polynomial time…