Related papers: Commutative automata networks
How do cellular automata behave in the limit of a very large number of cells? Is there a continuum limit with simple properties? We attack this problem by mapping certain classes of automata to quantum field theories for which powerful…
Cellular automata (CA) consist of an array of identical cells, each of which may take one of a finite number of possible states. The entire array evolves in discrete time steps by iterating a global evolution G. Further, this global…
The emergent dynamics in spacetime diagrams of cellular automata (CAs) is often organised by means of a number of behavioural classes. Whilst classification of elementary CAs is feasible and well-studied, non-elementary CAs are generally…
This paper aims at setting the keystone of a prospective theoretical study on the role of non-monotone interactions in biological regulation networks. Focusing on discrete models of these networks, namely, Boolean automata networks, we…
Quantum cellular automata (QCA) are reviewed, including early and more recent proposals. QCA are a generalization of (classical) cellular automata (CA) and in particular of reversible CA. The latter are reviewed shortly. An overview is…
We investigate networks of automata that synchronise over common action labels. A graph synchronisation topology between the automata is defined in such a way that two automata are connected iff they can synchronise over an action. We show…
Quantum computing is concerned with computer technology based on the principles of quantum mechanics, with operations performed at the quantum level. Quantum computational models make it possible to analyze the resources required for…
In this paper, we consider coordinated movement of a network of vehicles consisting of a bounded number of malicious agents, that is, vehicles must reach consensus in longitudinal position and a common predefined velocity. The motions of…
Random Boolean networks have been used widely to explore aspects of gene regulatory networks. A modified form of the model through which to systematically explore the effects of increasing the number of gene states has previously been…
We cast new light on the existing models of one-way deterministic topological automata by introducing a fresh but general, convenient model, in which, as each input symbol is read, an interior system of an automaton, known as a…
Consider a distributed task where the communication network is fixed but the local inputs given to the nodes of the distributed system may change over time. In this work, we explore the following question: if some of the local inputs…
We study the stability of orbits in large Boolean networks with given complex topology. We impose no restrictions on the form of the update rules, which may be correlated with local topological properties of the network. While recent past…
Cellular automata are a discrete dynamical system which models massively parallel computation. Much attention is devoted to computations with small time complexity for which the parallelism may provide further possibilities. In this paper,…
Quantum computation based on quantum cellular automata (QCA) can greatly reduce the control and precision necessary for experimental implementations of quantum information processing. A QCA system consists of a few species of qubits in…
Group cellular automata are continuous, shift-commuting endomorphisms of $G^\mathbb{Z}$, where $G$ is a finite group. We provide an easy-to-check characterization of expansivity for group cellular automata on abelian groups and we prove…
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…
Boolean networks are a general model of interacting entities, with applications to biological phenomena such as gene regulation. Attractors play a central role, and the schedule of entities update is a priori unknown. This article presents…
Quantum Cellular Automata are unitary maps that preserve locality and respect causality. We identify them, in any dimension, with simple tensor networks (PEPU) whose bond dimension does not grow with the system size. As a result, they…
Let L:= Z^D be the D-dimensional lattice and let A^L be the Cantor space of L-indexed configurations in some finite alphabet A, with the natural L-action by shifts. A `cellular automaton' is a continuous, shift-commuting self-map F of A^L,…
Alternating automata have been widely used to model and verify systems that handle data from finite domains, such as communication protocols or hardware. The main advantage of the alternating model of computation is that complementation is…