Related papers: Universal groups of cellular automata
Consider any sequence of finite groups $A^t$, where $t$ takes values in an integer index set $\mathbf{Z}$. A group system $A$ is a set of sequences with components in $A^t$ that forms a group under componentwise addition in $A^t$, for each…
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…
Finite cellular automata (FCA) are widely used in simulating nonlinear complex systems, and their reversibility is closely related to information loss during the evolution. However, only a relatively small portion of their reversibility…
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…
We study one-dimensional reversible and number-conserving cellular automata (RNCCA) that have both properties of reversibility and number-conservation. In the case of 2-neighbor RNCCA, Garc\'ia-Ramos proved that every RNCCA shows trivial…
There exist f.g.-universal cellular automata groups which are quotients of $\mathbb{Z} * \mathbb{Z}_2$ or $\mathbb{Z}_2 * \mathbb{Z}_2 * \mathbb{Z}_2$, as previously conjectured by the author.
Gottschalk's surjunctivity conjecture for a group $G$ states that it is impossible for cellular automata (CA) over the universe $G$ with finite alphabet to produce strict embeddings of the full shift into itself. A group universe $G$…
For a finite group $G$ and a finite set $A$, we study various algebraic aspects of cellular automata over the configuration space $A^G$. In this situation, the set $\text{CA}(G;A)$ of all cellular automata over $A^G$ is a finite monoid…
Relation between global transition function and local transition function of a homogeneous one dimensional cellular automaton (CA) is investigated for some standard transition functions. It could be shown that left shift and right shift CA…
Motivated by the search for idempotent cellular automata (CA), we study CA that act almost as the identity unless they read a fixed pattern $p$. We show that constant and symmetrical patterns always produce idempotent CA, and we…
We investigate quantum cellular automata (QCA) on one-dimensional spin systems defined over a subalgebra of the full local operator algebra - the symmetric subalgebra under a finite Abelian group symmetry $G$. For systems where each site…
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)…
For any group $G$ and any set $A$, a cellular automaton (CA) is a transformation of the configuration space $A^G$ defined via a finite memory set and a local function. Let $\text{CA}(G;A)$ be the monoid of all CA over $A^G$. In this paper,…
In this article we consider semigroups of transformations of cellular automata which act on a fixed shift space. In particular, we are interested in two properties of these semigroups which relate to "largeness". The first property is ID…
The notion of an automaton over a changing alphabet $X=(X_i)_{i\geq 1}$ is used to define and study automorphism groups of the tree $X^*$ of finite words over $X$. The concept of bi-reversibility for Mealy-type automata is extended to…
A class of additive cellular automata (ACA) on a finite group is defined by an index-group $\m g$ and a finite field $\m F_p$ for a prime modulus $p$ \cite{Bul_arch_1}. This paper deals mainly with ACA on infinite commutative groups and…
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…
This paper addresses the torsion problem for a class of automaton semigroups, defined as semigroups of transformations induced by Mealy automata, aka letter-by-letter transducers with the same input and output alphabet. The torsion problem…
Number-conserving cellular automata (NCCA) are particularly interesting, both because of their natural appearance as models of real systems, and because of the strong restrictions that number-conservation implies. Here we extend the…
Since first introduced by John von Neumann, the notion of cellular automaton has grown into a key concept in computer science, physics and theoretical biology. In its classical setting, a cellular automaton is a transformation of the set of…