Related papers: Mean equicontinuity and mean sensitivity on cellul…
We study the phase diagram and the critical behavior of a one-dimensional radius-1 two-state totalistic probabilistic cellular automaton having two absorbing states. This system exhibits a first-order phase transition between the fully…
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…
Cellular automata provide a fascinating class of dynamical systems capable of diverse complex behavior. These include simplified models for many phenomena seen in nature. Among other things, they provide insight into self-organized…
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…
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…
In this article, we consider a topological dynamical system. The generic limit set is the smallest closed subset which has a comeager realm of attraction. We study some of its topological properties, and the links with equicontinuity and…
We introduce a quantum cellular automaton that achieves approximate phase-covariant cloning of qubits. The automaton is optimized for 1-to-2N economical cloning. The use of the automaton for cloning allows us to exploit different foliations…
Bijections between sets may be seen as discrete (or crisp) unitary transformations used in quantum computations. So discrete quantum cellular automata are cellular automata with reversible transition functions. This note studies on 1d…
In this paper we study multi-sensitivity and thick sensitivity for continuous surjective selfmaps on compact metric spaces. We show that multi-sensitivity implies thick sensitivity, and the converse holds true for transitive systems. Our…
Two cellular automata are strongly conjugate if there exists a shift-commuting conjugacy between them. We prove that the following two sets of pairs $(F,G)$ of one-dimensional one-sided cellular automata over a full shift are recursively…
We study cellular automata on regular rooted trees. This includes the characterization of sofic tree shifts in terms of unrestricted Rabin automata and the decidability of the surjectivity problem for cellular automata between sofic tree…
A deterministic finite (semi)automaton is primitive if its transition monoid (semigroup) acting on the set of states has no non-trivial congruences. It is synchronizing if it contains a constant map (transformation). In analogy to…
In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows for calculating cell-wise probability distributions over…
We study three models of driven sandpile-type automata in the presence of quenched random defects. When the dynamics is conservative, all these models, termed the random sites (A), random bonds (B), and random slopes (C), self-organize into…
Countable state Markov shifts are a natural generalization of the well-known subshifts of finite type. They are the subject of current research both for their own sake and as models for smooth dynamical systems. In this paper, we…
We investigate the (non)-existence of universal automata for some classes of automata, such as finite automata and pushdown automata, and in particular the influence of the representation and encoding function. An alternative approach,…
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…
Certain fermionic quantum field theories are equivalent to probabilistic cellular automata, with fermionic occupation numbers associated to bits. We construct an automaton that represents a discrete model of spinor gravity in four…
We investigate the conditions under which the mean-field formulation of a probabilistic, totalistic cellular automaton approximates the logistic equation. We show that this goal can be only fulfilled for an infinite-range neighborhood. We…
We consider hexagonal cellular automata with immediate cell neighbourhood and three cell-states. Every cell calculates its next state depending on the integral representation of states in its neighbourhood, i.e. how many neighbours are in…