相关论文: Asymptotic Behaviour and Ratios of Complexity in C…

This paper studies two kinds of simulation between cellular automata: simulations based on factor and simulations based on sub-automaton. We show that these two kinds of simulation behave in two opposite ways with respect to the complexity…

The local structure theory for cellular automata (CA) can be viewed as an finite-dimensional approximation of infinitely-dimensional system. While it is well known that this approximation works surprisingly well for some cellular automata,…

We search for regularities in the sequences of numbers of preimages for elementary cellular automata. For 46 out of 88 "minimal" rules, we find recognizable patterns, usually in the form of second order recurrence equations with constant…

We study the classification of cellular-automaton update rules into Wolfram's four classes. We start with the notion of the input entropy of a spatiotemporal block in the evolution of a cellular automaton, and build on it by introducing two…

We study one dimensional binary Probabilistic Cellular Automaton (PCA) that interpolate between Wolfram's classical rules 23, 77, 178 and 232. These rules are the only ones that satisfy two criteria: (i) in the case of a majority in the…

Cellular Automata (CA) theory is a discrete model that represents the state of each of its cells from a finite set of possible values which evolve in time according to a pre-defined set of transition rules. CA have been applied to a number…

Using Rule 126 elementary cellular automaton (ECA) we demonstrate that a chaotic discrete system --- when enriched with memory -- hence exhibits complex dynamics where such space exploits on an ample universe of periodic patterns induced…

Symmetry resolved entanglement and entanglement asymmetry are two measures of quantum correlations sensitive to symmetries of the system. Here we discuss their non-equilibrium dynamics in the Rule 54 cellular automaton, a simple, yet…

We present a method to eliminate redundancy in the transition tables of Boolean automata: schema redescription with two symbols. One symbol is used to capture redundancy of individual input variables, and another to capture permutability in…

Wolfram has provided a qualitative classification of cellular automata(CA) rules according to which, there exits a class of CA rules (called Class 4) which exhibit complex pattern formation and long-lived dynamical activity (long…

Classical Cellular Automata (CCAs) are a powerful computational framework for modeling global spatio-temporal dynamics with local interactions. While CCAs have been applied across numerous scientific fields, identifying the local rule that…

We study one-dimensional cellular automata whose rules are chosen at random from among $r$-neighbor rules with a large number $n$ of states. Our main focus is the asymptotic behavior, as $n \to \infty$, of the longest temporal period…

In cellular automata with memory, the unchanged maps of the conventional cellular automata are applied to cells endowed with memory of their past states in some specified interval. We implement Rule 30 automata with a majority memory and…

Cellular automata (CA) are dynamical systems on symbolic configurations on the lattice. They are also used as models of massively parallel computers. As dynamical systems, one would like to understand the effect of small random…

We study the effect of topology variation on the dynamic behavior of a system with local update rules. We implement one-dimensional binary cellular automata on graphs with various topologies by formulating two sets of degree-dependent…

In this work we study the collective behaviors arising in a model of a simplified homogeneous society. Each agent is modeled as a binary ``perceptron'', receiving neighbors' opinions as inputs and outputting one of two possible opinions,…

Large Language Models (LLMs), trained solely on massive text data, have achieved high performance on the Winograd Schema Challenge (WSC), a benchmark proposed to measure commonsense knowledge and reasoning abilities about the real world.…

We present an intuitive formalism for implementing cellular automata on arbitrary topologies. By that means, we identify a symmetry operation in the class of elementary cellular automata. Moreover, we determine the subset of topologically…

We have considered the complexity and asymptotic stability in the process of biochemical substance exchange in a coupled ring of cells. We have used coupled maps to model this process. It includes the coupling parameter, cell affinity and…

We study the predictability of emergent phenomena in complex systems. Using nearest neighbor, one-dimensional Cellular Automata (CA) as an example, we show how to construct local coarse-grained descriptions of CA in all classes of Wolfram's…