Elementary, finite and linear vN-regular cellular automata

Elementary, Finite and Linear vN-Regular Cellular Automata

Let $G$ be a group and $A$ a set. A cellular automaton (CA) $\tau$ over $A^G$ is von Neumann regular (vN-regular) if there exists a CA $\sigma$ over $A^G$ such that $\tau \sigma\tau = \tau$, and in such case, $\sigma$ is called a generalised inverse of $\tau$. In this paper, we investigate vN-regularity of various kinds of CA. First, we establish that, over any nontrivial configuration space, t...

Linear Cellular Automata and Finite Automata

Linear cellular automata have a canonical representation in terms of labeled de Bruijn graphs. We will show that these graphs, construed as semiautomata, provide a natural setting for the study of cellular automata. For example, we give a simple algorithm to determine reversibility and surjectivity of the global maps. We also comment on Wolfram’s question about the growth rates of the minimal f...

Cellular Automata: Elementary Cellular Automata

Cellular automata (CA) are discrete dynamical systems consist of a regular finite grid of cell; each cell encapsulating an equal portion of the state, and arranged spatially in a regular fashion to form an n-dimensional lattice. A cellular automata is like computers, data represented by initial configurations which is processed by time evolution to produce output. This paper is an empirical stu...

Regular Languages and Finite Automata

Regular Languages and Finite Automata

In 1943, McCulloch and Pitts [4] published a pioneering work on a model for studying the behavior of the nervous systems. Following up on the ideas of McCulloch and Pitts, Kleene [3] wrote the first paper on finite automata and regular expressions. A finite automaton can be considered as the simplest machine model in that the machine has a finite memory; that is, the memory size is independent ...