Related papers: Cellular Automata Using Infinite Computations
Many different definitions of computational universality for various types of dynamical systems have flourished since Turing's work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical…
We discuss cellular automata over arbitrary finitely generated groups. We call a cellular automaton post-surjective if for any pair of asymptotic configurations, every pre-image of one is asymptotic to a pre-image of the other. The well…
Cayley graphs have a number of useful features: the ability to graphically represent finitely generated group elements and their relations; to name all vertices relative to a point; and the fact that they have a well-defined notion of…
Generalizing the motion representation we introduced for number-conserving rules, we give a systematic way to construct a generalized motion representation valid for non-conservative rules using the expression of the current, which appears…
Cellular automata are capable of developing complex behaviors based on simple local interactions between their elements. Some of these characteristics have been used to propose and improve meta-heuristics for global optimization; however,…
Infinite words, also known as streams, hold significant interest in computer science and mathematics, raising the natural question of how their complexity should be measured. We introduce cellular automaton reducibility as a measure of…
We introduce the property of pre-expansivity for cellular automata (CA): it is the property of being expansive on asymptotic pairs of configurations (i.e. configurations that differ in only finitely many positions). Pre-expansivity…
In this paper I present a first attempt for a possible description of fluids dynamics by mean of a cellular automata technique. With the use of simple and elementary rules, based on random behaviour either, the model permits to obtain the…
This is Chapter 24 in the "AutoMathA" handbook. Finite automata have been used effectively in recent years to define infinite groups. The two main lines of research have as their most representative objects the class of automatic groups…
A digit function is presented which provides the $i$th-digit in base $p$ of any real number $x$. By means of this function, formulated within $\mathcal{B}$-calculus, the local, nonlocal and global dynamical behaviors of cellular automata…
A recently introduced cellular automaton model for the description of traffic flow is investigated. It generalises asymmetric exclusion models which have attracted a lot of interest in the past. We calculate the so-called fundamental…
The emerging field of Nominal Computation Theory is concerned with the theory of Nominal Sets and its applications to Computer Science. We investigate here the impact of nominal sets on the definition of Cellular Automata and on their…
A number-conserving cellular automaton is a simplified model for a system of interacting particles. This paper contains two related constructions by which one can find all one-dimensional number-conserving cellular automata with one kind of…
Cellular automata are dynamical systems defined on lattices and commuting with the Bernoulli shift. In this work, we focus on the spectral properties of D-dimensional cellular automata. We give a characterization of their spectrum from both…
Cellular automata (CA) consist of an array of identical cells, each of which may take one of a finite number of possible states. The entire array evolves in discrete time steps by iterating a global evolution G. Further, this global…
Cellular automata (CA) is an important modelling paradigm for complex systems. In the design of cellular automata, the most difficult task is to find the transformation rules that describe the temporal evolution or pattern of a modelled…
We consider quantum cellular automata for one-dimensional chains of Fermionic modes and study their implementability as finite depth quantum circuits. Fermionic automata have been classified in terms of an index modulo circuits and the…
In programming language semantics, it has proved to be fruitful to analyze context-dependent notions of computation, e.g., dataflow computation and attribute grammars, using comonads. We explore the viability and value of similar modeling…
In this dissertation, we study temporally stochasticity in cellular automata and the behavior of such cellular automata. The work also explores the computational ability of such cellular automaton that illustrates the computability of…
In this paper we propose a rule-independent description of applications of cellular automata rules for one-dimensional additive cellular automata on cylinders of finite sizes. This description is shown to be a useful tool for for answering…