Related papers: Cellular automata in operational probabilistic the…
This paper introduces a new formalism for quantum cellular automata (QCAs), based on evolving tensor products of qubits using local unitary operators. It subsequently uses this formalism to analyze and validate several conjectures, stemming…
Models of areas of physics in terms of cellular automata have become increasingly popular. Cellular automata (CAs) support the modeling of systems with discrete state component values and enforce the comprehensive specification of the…
An introduction to cellular automata (both deterministic and probabilistic) with examples. Definition of deterministic automata, dynamical properties, damage spreading and Lyapunov exponents; probabilistic automata and Markov processes,…
Probabilistic cellular automata with deterministic updating are quantum systems. We employ the quantum formalism for an investigation of random probabilistic cellular automata, which start with a probability distribution over initial…
We define the class of rapidly left expansive cellular automata, which contains fractional multiplication automata, Wolfram's Rule 30, and many others. The definition has been shaped by a proposition of Jen on aperiodicity of columns in…
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…
This talk advocates intrinsic universality as a notion to identify simple cellular automata with complex computational behavior. After an historical introduction and proper definitions of intrinsic universality, which is discussed with…
Over an arbitrary commutative ring $R$, we develop a theory of quantum cellular automata. We then use algebraic K-theory to construct a space $\mathbf{Q}(X)$ of quantum cellular automata (QCA) on a given metric space $X$. In most cases of…
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…
This paper deals with the theory and application of 2-Dimensional, nine-neighborhood, null- boundary, uniform as well as hybrid Cellular Automata (2D CA) linear rules in image processing. These rules are classified into nine groups…
We show that a large number of elementary cellular automata are computationally simple. This work is the first systematic classification of elementary cellular automata based on a formal notion of computational complexity. Thanks to the…
We introduce an action principle for a class of integer valued cellular automata and obtain Hamiltonian equations of motion. Employing sampling theory, these discrete deterministic equations are invertibly mapped on continuum equations for…
This article presents a new characterization of controllability and regional controllability of Deterministic Cellular Automata (CA for short). It focuses on analyzing these problems within the framework of control theory, which have been…
The essential ingredient for studying the phenomena of emergence is the ability to generate and manipulate emergent systems that span large scales. Cellular automata are the model class particularly known for their effective scalability but…
The donation game is a well-established framework for studying the emergence and evolution of cooperation in multi-agent systems. The cooperative behavior can be influenced by the environmental noise in partially observable settings and by…
This paper presents a new framework for asynchrony. This has its origins in our attempts to better harness the internal decision making process of cellular automata (CA). Thus, we show that a max-plus algebraic model of asynchrony arises…
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.…
We study self-similarity in one-dimensional probabilistic cellular automata (PCA) using the renormalization technique. We introduce a general framework for algebraic construction of renormalization groups (RG) on cellular automata and apply…
The Game of Life (GoL), one well known 2D cellular automaton, does not typically ensure interesting long-term phenotypic dynamics. Therefore, while being Turing complete, GoL cannot be said to be open-ended. In this work, we extend GoL with…
In this paper, linear Cellular Automta (CA) rules are recursively generated using a binary tree rooted at "0". Some mathematical results on linear as well as non-linear CA rules are derived. Integers associated with linear CA rules are…