相关论文: Asymptotic Behaviour and Ratios of Complexity in C…
This paper studies complexity of recognition of classes of bounded configurations by a generalization of conventional cellular automata (CA) -- finite dynamic cellular automata (FDCA). Inspired by the CA-based models of biological and…
The emergence of complex behaviors in cellular automata is an area that has been widely developed in recent years with the intention to generate and analyze automata that produce space-moving patterns or gliders that interact in a periodic…
We explore the emergence of intelligent behavior in artificial systems by investigating how the complexity of rule-based systems influences the capabilities of models trained to predict these rules. Our study focuses on elementary cellular…
We study cellular automata with respect to a new communication complexity problem: each of two players know half of some finite word, and must be able to tell whether the state of the central cell will follow a given evolution, by…
Cellular Automata (CA) are discrete dynamical systems and an abstract model of parallel computation. The limit set of a cellular automaton is its maximal topological attractor. A well know result, due to Kari, says that all nontrivial…
The model of cellular automata is fascinating because very simple local rules can generate complex global behaviors. The relationship between local and global function is subject of many studies. We tackle this question by using results on…
This paper introduces a simple formalism for dealing with deterministic, non- deterministic and stochastic cellular automata in an unified and composable manner. This formalism allows for local probabilistic correlations, a feature which is…
We introduce CellARC, a synthetic benchmark for abstraction and reasoning built from multicolor 1D cellular automata (CA). Each episode has five support pairs and one query serialized in 256 tokens, enabling rapid iteration with small…
Cellular automata are fully-discrete, spatially-extended dynamical systems that evolve by simultaneously applying a local update function. Despite their simplicity, the induced global dynamic produces a stunning array of richly-structured,…
In order to develop systems capable of modeling artificial life, we need to identify, which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time…
The complexity of cellular automata is traditionally measured by their computational capacity. However, it is difficult to choose a challenging set of computational tasks suitable for the parallel nature of such systems. We study the…
We discuss a characterization of complexity based on successive approximations of the probability density describing a system by means of maximum entropy methods, thereby quantifying the respective role played by different orders of…
We study the generic limit sets of one-dimensional cellular automata, which intuitively capture their asymptotic dynamics while discarding transient phenomena. As our main results, we characterize the automata whose generic limit set is a…
Cellular automata (CAs) are dynamical systems which exhibit complex global behavior from simple local interaction and computation. Since the inception of cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention of…
We numerically study the dynamics of elementary 1D cellular automata (CA), where the binary state $\sigma_i(t) \in \{0,1\}$ of a cell $i$ does not only depend on the states in its local neighborhood at time $t-1$, but also on the memory of…
The asymptotic behavior of a cellular automaton iterated on a random configuration is well described by its limit probability measure(s). In this paper, we characterize measures and sets of measures that can be reached as limit points after…
In this paper we propose an approach for measuring growth of complexity of emerging patterns in complex systems such as cellular automata. We discuss several ways how a metric for measuring the complexity growth can be defined. This…
Cellular automata (CA) are discrete-time dynamical systems with local update rules on a lattice. Despite their elementary definition, CA support a wide spectrum of macroscopic phenomena central to statistical physics: equilibrium and…
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 $\lambda$.…
We propose some conjectures for asymptotic distribution of probabilistic Burgers cellular automaton (PBCA) which is defined by a simple motion rule of particles including a probabilistic parameter. Asymptotic distribution of configurations…