Related papers: Traced communication complexity of cellular automa…
The expanding cellular automata (XCA) variant of cellular automata is investigated and characterized from a complexity-theoretical standpoint. An XCA is a one-dimensional cellular automaton which can dynamically create new cells between…
Emergent processes in complex systems such as cellular automata can perform computations of increasing complexity, and could possibly lead to artificial evolution. Such a feat would require scaling up current simulation sizes to allow for…
Studies of quantum computer implementations suggest cellular quantum computer architectures. These architectures can simulate the evolution of quantum cellular automata, which can possibly simulate both quantum and classical physical…
Cellular automata provide a fascinating class of dynamical systems capable of diverse complex behavior. These include simplified models for many phenomena seen in nature. Among other things, they provide insight into self-organized…
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…
We evaluate new complexity measures on the symbolic dynamics of coupled tent maps and cellular automata. These measures quantify complexity in terms of $k$-th order statistical dependencies that cannot be reduced to interactions between…
We show techniques of analyzing complex dynamics of cellular automata (CA) with chaotic behaviour. CA are well known computational substrates for studying emergent collective behaviour, complexity, randomness and interaction between order…
Communication complexity is an area of classical computer science which studies how much communication is necessary to solve various distributed computational problems. Quantum information processing can be used to reduce the amount of…
Particle-like objects are observed to propagate and interact in many spatially extended dynamical systems. For one of the simplest classes of such systems, one-dimensional cellular automata, we establish a rigorous upper bound on the number…
Hierarchical structure is an essential part of complexity, important notion relevant for a wide range of applications ranging from biological population dynamics through robotics to social sciences. In this paper we propose a simple…
Cellular automata (CAs) are fully-discrete dynamical models that have received much attention due to the fact that their relatively simple setup can nonetheless express highly complex phenomena. Despite the model's theoretical maturity and…
Deep learning techniques have recently demonstrated broad success in predicting complex dynamical systems ranging from turbulence to human speech, motivating broader questions about how neural networks encode and represent dynamical rules.…
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…
A new class of automata networks is defined. Their evolution rules are determined by a probability measure p on the set of all integers Z and an indicator function I_A on the interval [0,1]. It is shown that any cellular automaton rule can…
Number-conserving (or {\em conservative}) cellular automata have been used in several contexts, in particular traffic models, where it is natural to think about them as systems of interacting particles. In this article we consider several…
To identify potential universal cellular automata, a method is developed to measure information processing capacity of elementary cellular automata. We consider two features of cellular automata: Ability to store information, and ability to…
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…
Commonly studied cellular automata are memoryless and have fixed topology of connections between cells. However by allowing updates of links and short-term memory in cells we may potentially discover novel complex regimes of spatio-temporal…
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…
The control of chaotic systems implies inducing an unpredictable system to follow a desired trajectory using the smallest "force". In low-dimensional continuous systems, one method is that of reconstructing the tangent space, so that the…