Related papers: No weakly factor-universal cellular automaton
We prove that the set of subgroups of the automorphism group of a two-sided full shift is closed under countable graph products. We introduce the notion of a group action without $A$-cancellation (for an abelian group $A$), and show that…
Let $G$ be a group and let $X$ be an algebraic variety over an algebraically closed field $k$ of characteristic zero. Denote $A=X(k)$ the set of rational points of $X$. We investigate invertible algebraic cellular automata $\tau \colon A^G…
This paper studies three classes of cellular automata from a computational point of view: freezing cellular automata where the state of a cell can only decrease according to some order on states, cellular automata where each cell only makes…
This paper investigates the conditions under which a given circular (synchronizing) DFA is \emph{simple} (sometimes referred to as \emph{primitive}) and when it is \emph{irreducible}. Our notion of irreducibility slightly differs from the…
Harvey Friedman's $ \mathsf{WD} $ is a weak set theory given by the following non-logical axioms: $ \mathsf{(W)} \; \forall x y \, \exists z \, \forall u \left[ \, u \in z \leftrightarrow ( \, u \in x \; \vee \; u = y \, ) \, \right] $; $…
We show that an almost expansive cellular automaton according to Gilman's classification cannot have irrational eigenvalues. This completes the proof that any surjective cellular automaton cannot have irrational eigenvalues for the uniform…
We show that any direction in the plane occurs as the unique non-expansive direction of a \mathbb{Z}^{2} action, answering a question of Boyle and Lind. In the case of rational directions, the subaction obtained is non-trivial. We also…
The orbit closures of regular model sets generated from a cut-and-project scheme given by a co-compact lattice $\mathcal{L}\subset G\times H$ and compact and aperiodic window $W\subseteq H$, have the maximal equicontinuous factor (MEF)…
Automata networks are mappings of the form f : Q Z $\rightarrow$ Q Z , where Q is a finite alphabet and Z is a set of entities; they generalise Cellular Automata and Boolean networks. An update schedule dictates when each entity updates its…
In this paper, we prove that there is a strongly universal cellular automaton in the dodecagrid, the tesselllation {5,3,4} of the hyperbolic 3D space, with four states but, it is not rotation invariant as the automaton of arXiv:2104.01561…
The cellular automaton is a widely known model of both reversible and irreversible computations. The family of reversible second-order cellular automata considered in this work is appropriate both for construction of logic gates and…
A cellular automaton named Rule 184++C is proposed as a meta-model to investigate the flow of various complex particles. In this model, unlike the granular pipe flow and the traffic flow, not only the free-jam phase transition but also the…
If a locally cartesian closed category carries a weak factorisation system, then the left maps are stable under pullback along right maps if and only if the right maps are closed under pushforward along right maps. We refer to this…
We present a preliminary results of our Galactic Habitable Zone (GHZ) 2D probabilistic cellular automata models. The relevant time-scales (emergence of life, it's diversification and evolution influenced with the global risk function) are…
We study $2$-neighbor one-dimensional cellular automata with a large number $n$ of states and randomly selected rules. We focus on the rules with weakly robust periodic solutions (WRPS). WRPS are global configurations that exhibit spatial…
Quantum cellular automata are alternative quantum-computing paradigms to quantum Turing machines and quantum circuits. Their working mechanisms are inherently automated, therefore measurement free, and they act in a translation invariant…
We present a direct transformation of weak alternating $\omega$-automata into equivalent backward deterministic $\omega$-automata and show (1) how it can be used to obtain a transformation of non-deterministic B\"uchi automata into…
In this paper, we prove that there is a strongly universal cellular automaton on the pentagrid with six states. For each cell c, Moore neighbourhood consists of the cells which share a vertex with c. Moreover, the rules are rotation…
This paper investigates the $k$-mixing property of a multidimensional cellular automaton. Suppose $F$ is a cellular automaton with the local rule $f$ defined on a $d$-dimensional convex hull $\mathcal{C}$ which is generated by an apex set…
The properties of two-state nearest-neighbour cellular automata (CA) that are capable of density classification are discussed. It is shown that these CA actually conserve the total density, rather than merely classifying it. This is also…