相关论文: Spectral domain boundaries in cellular automata
This paper explores the algebraic conditions under which a cellular automaton with a non-linear local rule exhibits surjectivity and reversibility. We also analyze the role of permutivity as a key factor influencing these properties and…
If M is a monoid (e.g. the lattice Z^D), and A is an abelian group, then A^M is a compact abelian group; a linear cellular automaton (LCA) is a continuous endomorphism F:A^M --> A^M that commutes with all shift maps. If F is diffusive, and…
We consider quantum cellular automata for one-dimensional chains of Fermionic modes and study their implementability as finite depth quantum circuits. Fermionic automata have been classified in terms of an index modulo circuits and the…
The goal of this paper is to show why the framework of communication complexity seems suitable for the study of cellular automata. Researchers have tackled different algorithmic problems ranging from the complexity of predicting to the…
Gauge-invariance is a fundamental concept in physics---known to provide the mathematical justification for all four fundamental forces. In this paper, we provide discrete counterparts to the main gauge theoretical concepts, directly in…
Let $G$ be a group and let $X$ be an algebraic variety over an algebraically closed field $k$ of characteristic zero. Denote $A=X(k)$ the set of rational points of $X$. We investigate invertible algebraic cellular automata $\tau \colon A^G…
Cellular Automata are discrete--time dynamical systems on a spatially extended discrete space which provide paradigmatic examples of nonlinear phenomena. Their stochastic generalizations, i.e., Probabilistic Cellular Automata, are discrete…
We consider discrete and integer-valued cellular automata (CA). A particular class of which comprises "Hamiltonian CA" with equations of motion that bear similarities to Hamilton's equations, while they present discrete updating rules. The…
The generic limit set of a topological dynamical system of the smallest closed subset of the phase space that has a comeager realm of attraction. It intuitively captures the asymptotic dynamics of almost all initial conditions. It was…
Recent advances on quantum foundations achieved the derivation of free quantum field theory from general principles, without referring to mechanical notions and relativistic invariance. From the aforementioned principles a quantum cellular…
A cellular automaton (CA) is a parallel synchronous computing model, which consists in a juxtaposition of finite automata (cells) whose state evolves according to that of their neighbors. Its trace is the set of infinite words representing…
In addition to the $\lambda$ parameter, we have found another parameter which characterize the class III, class II and class IV patterns more quantitatively. It explains why the different classes of patterns coexist at the same $\lambda$.…
Conformal invariance is spontaneously broken in many physical systems leading to the appearance of a single massless Goldstone mode in the spectrum, the dilaton. The dilaton soft limit is shown to generically encode the action of both the…
We consider two relatively natural topologizations of the set of all cellular automata on a fixed alphabet. The first turns out to be rather pathological, in that the countable space becomes neither first-countable nor sequential. Also,…
Cellular automata are topological dynamical systems. We consider the problem of deciding whether two cellular automata are conjugate or not. We also consider deciding strong conjugacy, that is, conjugacy by a map that commutes with the…
One-dimensional quantum cellular automata (QCA) consist in a line of identical, finite dimensional quantum systems. These evolve in discrete time steps according to a local, shift-invariant unitary evolution. By local we mean that no…
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,…
In this paper a model of subscriber telephone network based on the concept of cellular automata is elaborated. Some fractal properties inherent in the model are revealed that vary depending on parameters assigning its operation rules. The…
A transition from asymmetric to symmetric patterns in time-dependent extended systems is described. It is found that one dimensional cellular automata, started from fully random initial conditions, can be forced to evolve into complex…
While one-dimensional cellular automata have been well studied, there are relatively few results about multidimensional cellular automata; the investigation of cellular automata defined on Cayley trees constitutes an intermediate class.…