Related papers: Von Neumann Regular Cellular Automata
We give a one-dimensional quantum cellular automaton (QCA) capable of simulating all others. By this we mean that the initial configuration and the local transition rule of any one-dimensional QCA can be encoded within the initial…
We investigate the mean dimension of a cellular automaton (CA for short) with a compact non-discrete space of states. A formula for the mean dimension is established for (near) strongly permutative, permutative algebraic and unit…
We study two-dimensional rotation-symmetric number-conserving cellular automata working on the von Neumann neighborhood (RNCA). It is known that such automata with 4 states or less are trivial, so we investigate the possible rules with 5…
This paper explores the algebraic conditions under which a cellular automaton with a non-linear local rule exhibits surjectivity and reversibility. We also analyze the role of permutivity as a key factor influencing these properties and…
We study the generic limit sets of one-dimensional cellular automata, which intuitively capture their asymptotic dynamics while discarding transient phenomena. As our main results, we characterize the automata whose generic limit set is a…
Cellular Automaton (CA) and an Integral Value Transformation (IVT) are two well established mathematical models which evolve in discrete time steps. Theoretically, studies on CA suggest that CA is capable of producing a great variety of…
We study the most elementary family of cellular automata defined over an arbitrary group universe $G$ and an alphabet $A$: the lazy cellular automata, which act as the identity on configurations in $A^G$, except when they read a unique…
In this paper we introduce the concept of a Cayley graph automatic group (CGA group or graph automatic group, for short) which generalizes the standard notion of an automatic group. Like the usual automatic groups graph automatic ones enjoy…
This paper concerns the general problem of classifying the finite deterministic automata that admit a synchronizing (or reset) word. (For our purposes it is irrelevant if the automata has initial or final states.) Our departure point is the…
Reversibility of a one-dimensional finite cellular automaton (CA) is dependent on lattice size. A finite CA can be reversible for a set of lattice sizes. On the other hand, reversibility of an infinite CA, which is decided by exploring the…
We study sources of isomorphisms of additive cellular automata on finite groups (called index-group). It is shown that many isomorphisms (called regular) of automata are reducible to the isomorphisms of underlying algebraic structures (such…
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…
We describe a simple n-dimensional quantum cellular automaton (QCA) capable of simulating all others, in that the initial configuration and the forward evolution of any n-dimensional QCA can be encoded within the initial configuration of…
Every transitive cellular automaton (CA) is sensitive to initial conditions. We study this implication in the more general context of non-uniform cellular automata (NUCA) with finitely many different local update rules assigned to cells. We…
One-dimensional quantum cellular automata (QCA) consist in a line of identical, finite dimensional quantum systems. These evolve in discrete time steps according to a local, shift-invariant unitary evolution. By local we mean that no…
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 minimalistic model for chimera states is presented. The model is a cellular automaton (CA) which depends on only one adjustable parameter, the range of the nonlocal coupling, and is built from elementary cellular automata and the majority…
A quantum cellular automaton (QCA) is an abstract model consisting of an array of finite-dimensional quantum systems that evolves in discrete time by local unitary operations. Here we propose a simple coarse-graining map, where the spatial…
The notions of universality and completeness are central in the theories of computation and computational complexity. However, proving lower bounds and necessary conditions remains hard in most of the cases. In this article, we introduce…
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…