相关论文: Number conserving cellular automata: form decidabi…
Stochastic dynamics govern many important processes in cellular biology, and an underlying theoretical approach describing these dynamics is desirable to address a wealth of questions in biology and medicine. Mathematical tools exist for…
In a recent paper Sutner proved that the first-order theory of the phase-space $\mathcal{S}_\mathcal{A}=(Q^\mathbb{Z}, \longrightarrow)$ of a one-dimensional cellular automaton $\mathcal{A}$ whose configurations are elements of…
We study the class of asynchronous non-uniform cellular automata (ANUCA) over an arbitrary group universe with multiple local transition rules. We introduce the notion of stable injectivity, stable reversibility, stable post-surjectivity…
Step size in continuous cellular automata (CA) plays an important role in the stability and behavior of self-organizing patterns. Continous CA dynamics are defined by formula very similar to numerical estimation of physics-based ordinary…
In this paper we introduce a new quantum computation model, the linear quantum cellular automaton. Well-formedness is an essential property for any quantum computing device since it enables us to define the probability of a configuration in…
We say that a finite asynchronous cellular automaton (or more generally, any sequential dynamical system) is pi-independent if its set of periodic points are independent of the order that the local functions are applied. In this case, the…
Self-organizing complex systems can be modeled using cellular automaton models. However, the parametrization of these models is crucial and significantly determines the resulting structural pattern. In this research, we introduce and…
Topological transitivity is a fundamental notion in topological dynamics and is widely regarded as a basic indicator of global dynamical complexity. For general cellular automata, topological transitivity is known to be undecidable. By…
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…
We investigate the ability of a genetic algorithm to design cellular automata that perform computations. The computational strategies of the resulting cellular automata can be understood using a framework in which ``particles'' embedded in…
Cellular automata are topological dynamical systems. We consider the problem of deciding whether two cellular automata are conjugate or not. We also consider deciding strong conjugacy, that is, conjugacy by a map that commutes with the…
We provide algebraic criteria for the unitarity of linear quantum cellular automata, i.e. one dimensional quantum cellular automata. We derive these both by direct combinatorial arguments, and by adding constraints into the model which do…
State-of-the-art review of cellular automata, cellular automata for partial differential equations, differential equations for cellular automata and pattern formation in biology and engineering.
After an apparent hiatus of roughly 30 years, we revisit a seemingly neglected subject in the theory of (one-dimensional) cellular automata: sublinear-time computation. The model considered is that of ACAs, which are language acceptors…
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,…
In this paper I describe a cellular automaton model of a multi-species ecosystem, suitable for the study of emergent properties of macroevolution. Unlike majority of ecological models, the number of coexisting species is not fixed. Starting…
Counters that hold natural numbers are ubiquitous in modeling and verifying software systems; for example, they model dynamic creation and use of resources in concurrent programs. Unfortunately, such discrete counters often lead to…
Discrete dynamical systems can exhibit complex behaviour from the iterative application of straightforward local rules. A famous example are cellular automata whose global dynamics are notoriously challenging to analyze. To address this, we…
Cellular automata (CA) are dynamical systems defined by a finite local rule but they are studied for their global dynamics. They can exhibit a wide range of complex behaviours and a celebrated result is the existence of (intrinsically)…
This note is a survey of examples and results about cellular automata with the purpose of recalling that there is no 'universal' way of being computationally universal. In particular, we show how some cellular automata can embed efficient…