相关论文: Cellular Automata and Ultra-Discrete Painlev\'e Eq…
The probabilistic cellular automaton (PCA) method is highlighted for its relatively simple numerical algorithm and low computational cost in the simulation of microstructural evolution. In this method, probabilistic state change rules are…
The paper proposes a simple formalism for dealing with deterministic, non-deterministic and stochastic cellular automata in a unifying and composable manner. Armed with this formalism, we extend the notion of intrinsic simulation between…
The goal of this paper is to present a solution of the cellular automaton associated with the discrete KdV equation using algebro-geometric solution of the discrete KP equation over a finite field out of a hyperelliptic curve.
Bijections between sets may be seen as discrete (or crisp) unitary transformations used in quantum computations. So discrete quantum cellular automata are cellular automata with reversible transition functions. This note studies on 1d…
Cellular automata are a class of computational models based on simple rules and algorithms that can simulate a wide range of complex phenomena. However, when using conventional computers, these 'simple' rules are only encapsulated at the…
Cellular automata can show well known features of quantum mechanics, such as a linear rule according to which they evolve and which resembles a discretized version of the Schroedinger equation. This includes corresponding conservation laws.…
A universal map is derived for all deterministic 1D cellular automata (CA) containing no freely adjustable parameters. The map can be extended to an arbitrary number of dimensions and topologies and its invariances allow to classify all CA…
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…
This paper studies directional dynamics in cellular automata, a formalism previously introduced by the third author. The central idea is to study the dynamical behaviour of a cellular automaton through the conjoint action of its global rule…
Probabilistic cellular automata describe the dynamics of classical spin models, which, for sufficiently small temperature $T$, can serve as classical memory capable of storing information even in the presence of nonzero external magnetic…
We study probabilistic cellular automata (PCA) and quantum cellular automata (QCA) as frameworks for solving the Maximum Independent Set (MIS) problem. We first introduce a synchronous PCA whose dynamics drives the system toward the…
Cellular automata represent physical systems where both space and time are discrete, and the associated physical quantities assume a limited set of values. While previous research has applied cellular automata in modeling chemical,…
Spontaneous self-replication in cellular automata has long been considered rare, with most known examples requiring careful design or artificial initialization. In this paper, we present formal, causal evidence that such replication can…
We study discrete dynamical systems through the topological concepts of limit set, which consists of all points that can be reached arbitrarily late, and asymptotic set, which consists of all adhering values of orbits. In particular, we…
The theory of cellular automata in operational probabilistic theories is developed. We start introducing the composition of infinitely many elementary systems, and then use this notion to define update rules for such infinite composite…
Cellular Automata(CA) is a discrete computing model which provides simple, flexible and efficient platform for simulating complicated systems and performing complex computation based on the neighborhoods information. CA consists of two…
The dynamical behavior of non-uniform cellular automata is compared with the one of classical cellular automata. Several differences and similarities are pointed out by a series of examples. Decidability of basic properties like…
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…
Topological dynamics of cellular automata (CA), inherited from classical dynamical systems theory, has been essentially studied in dimension 1. This paper focuses on higher dimensional CA and aims at showing that the situation is different…
Topological dynamics of cellular automata (CA), inherited from classical dynamical systems theory, has been essentially studied in dimension 1. This paper focuses on 2D CA and aims at showing that the situation is different and more…