Related papers: Expansive Automata Networks
An automata network is a finite graph where each node holds a state from some finite alphabet and is equipped with an update function that changes its state according to the configuration of neighboring states. More concisely, it is given…
An automata network with $n$ components over a finite alphabet $Q$ of size $q$ is a discrete dynamical system described by the successive iterations of a function $f:Q^n\to Q^n$. In most applications, the main parameter is the interaction…
An automata network with $n$ components over a finite alphabet $Q$ of size $q$ is a discrete dynamical system described by the successive iterations of a function $f:Q^n\to Q^n$. In most applications, the main parameter is the interaction…
Automata networks are mappings of the form f : Q Z $\rightarrow$ Q Z , where Q is a finite alphabet and Z is a set of entities; they generalise Cellular Automata and Boolean networks. An update schedule dictates when each entity updates its…
An automata network (AN) is a finite graph where each node holds a state from a finite alphabet and is equipped with a local map defining the evolution of the state of the node depending on its neighbors. The global dynamics of the network…
An automata network is a graph of entities, each holding a state from a finite set and evolving according to a local update rule which depends only on its neighbors in the network's graph. It is freezing if there is an order on the states…
When we focus on finite dynamical systems from both the computability/complexity and the modelling standpoints, automata networks seem to be a particularly appropriate mathematical model on which theory shall be developed. In this paper,…
An automata network is a network of entities, each holding a state from a finite set and evolving according to a local update rule which depends only on its neighbors in the network's graph. It is freezing if there is an order on states…
The theory of finite automata concerns itself with words in a free monoid together with concatenation and without further structure. There are, however, important applications which use alphabets which are structured in some sense. We…
We introduce Network Automata, a framework which couples the topological evolution of a network to its structure. It is useful for dealing with networks in which the topology evolves according to some specified microscopic rules and,…
A deterministic finite automaton in which every non-empty set of states occurs as the image of the whole state set under the action of a suitable input word is called completely reachable. We characterize such automata in terms of graphs…
Automata networks, and in particular Boolean networks, are used to model diverse networks of interacting entities. The interaction graph of an automata network is its most important parameter, as it represents the overall architecture of…
A network provides powerful means of representing complex relationships between entities by abstracting entities as vertices, and relationships as edges connecting vertices in a graph. Beyond the presence or absence of relationships, a…
A complete deterministic finite automaton in which every non-empty subset of the state set occurs as the image of the whole state set under the action of a suitable input word is called completely reachable. We characterize completely…
Many graph algorithms can be viewed as sets of rules that are iteratively applied, with the number of iterations dependent on the size and complexity of the input graph. Existing machine learning architectures often struggle to represent…
Edge expansion is a parameter indicating how well-connected a graph is. It is useful for designing robust networks, analysing random walks or information flow through a network and is an important notion in theoretical computer science.…
Distributed automata are finite-state machines that operate on finite directed graphs. Acting as synchronous distributed algorithms, they use their input graph as a network in which identical processors communicate for a possibly infinite…
Extensions to finite-state automata on strings, such as multi-head automata or multi-counter automata, have been successfully used to encode many infinite-state non-regular verification problems. In this paper, we consider a generalization…
Automata networks are a versatile model of finite discrete dynamical systems composed of interacting entities (the automata), able to embed any directed graph as a dynamics on its space of configurations (the set of vertices, representing…
A dynamical network, a graph whose nodes are dynamical systems, is usually characterized by a large dimensional space which is not always accesible due to the impossibility of measuring all the variables spanning the state space. Therefore,…