Related papers: Generalized Cayley Graphs and Cellular Automata ov…
We introduce a family of graphs that generalises the class of Cayley graphs. For non-empty subsets L, R of a group G, the two-sided Cayley graph 2SC(G;L,R) is the directed graph with vertex set G and an arc from x to y if and only if…
Temporal graphs represent graph evolution over time, and have been receiving considerable research attention. Work on expressing temporal graph patterns or discovering temporal motifs typically assumes relatively simple temporal…
Let $G$ be a regular graph of degree $d$ and let $A\subset V(G)$. Say that $A$ is $\eta$-closed if the average degree of the subgraph induced by $A$ is at least $\eta d$. This says that if we choose a random vertex $x\in A$ and a random…
A few properties of unitary Cayley graphs are explored using their eigenvalues. It is shown that the adjacency algebra of a unitary Cayley graph is a coherent algebra. Finally, a class of unitary Cayley graphs that are distance regular are…
Any algorithm (in the sense of Gurevich's abstract-state-machine axiomatization of classical algorithms) operating over any arbitrary unordered domain can be simulated by a dynamic cellular automaton, that is, by a pattern-directed cellular…
Cellular Automata (CA), as they are presented in the literature, are abstract mathematical models of computation. In this pa- per we present an alternate approach: using the CA as a model or theory of physical systems and devices. While…
The original local, discrete example of Linear Unitary Cellular Automata (LUCA) is analyzed in terms of a new representation previously introduced in [1] for classical CA. Several important underlying symmetries are reviewed and their tight…
Classical Cellular Automata (CCAs) are a powerful computational framework widely used to model complex systems driven by local interactions. Their simplicity lies in the use of a finite set of states and a uniform local rule, yet this…
The growth function is the generating function for sizes of spheres around the identity in Cayley graphs of groups. We present a novel method to calculate growth functions for automatic groups with normal form recognizing automata that…
We investigate subsets of the symmetric group with structure similar to that of a graph. The trees of these subsets correspond to minimal conjugate generating sets of the symmetric group. There are two main theorems in this paper. The first…
Cellular automata are fully-discrete, spatially-extended dynamical systems that evolve by simultaneously applying a local update function. Despite their simplicity, the induced global dynamic produces a stunning array of richly-structured,…
Previous works have shown that contextual information can improve the performance of neural machine translation (NMT). However, most existing document-level NMT methods only consider a few number of previous sentences. How to make use of…
We propose a generalization of transformer neural network architecture for arbitrary graphs. The original transformer was designed for Natural Language Processing (NLP), which operates on fully connected graphs representing all connections…
Conceptual Graphs (CGs) are a formalism to represent knowledge. However producing a CG database is complex. To the best of our knowledge, existing methods do not fully use the expressivity of CGs. It is particularly troublesome as it is…
Graph Convolutional Neural Networks (Graph CNNs) are generalizations of classical CNNs to handle graph data such as molecular data, point could and social networks. Current filters in graph CNNs are built for fixed and shared graph…
This paper proposes a generalized framework for cellular automata using the language of category theory, extending the classical definition beyond set-theoretic constraints. For an arbitrary category $\mathscr{C}$ with products, we define…
Computers and algorithms play an ever-increasing role in obtaining new results in graph theory. In this survey, we present a broad range of techniques used in computer-assisted graph theory, including the exhaustive generation of all…
Recently, several works by a number of authors have studied integrality, distance integrality, and distance powers of Cayley graphs over some finite groups, such as dicyclic groups and (generalized) dihedral groups. Our aim is to generalize…
Cellular automata are a set of computational models in discrete space that have a discrete time evolution defined by neighbourhood rules. They are used to simulate many complex systems in physics and science in general. In this work,…
Bidirected graphs generalize directed and undirected graphs in that edges are oriented locally at every node. The natural notion of the degree of a node that takes into account (local) orientations is that of net-degree. In this paper, we…