Related papers: On Reversible Cellular Automata with Triplet Local…
In this dissertation, we study two of the global properties of 1-dimensional cellular automata (CAs) under periodic boundary condition, namely, reversibility and randomness. To address reversibility of finite CAs, we develop a mathematical…
This investigation studies the ergodic properties of reversible linear cellular automata over $\mathbb{Z}_m$ for $m \in \mathbb{N}$. We show that a reversible linear cellular automaton is either a Bernoulli automorphism or non-ergodic. This…
It is shown that irreversible classical cellular automata can be performed by quantum algorithm using additional ancilla registers. The algorithm for cellular automata states analysis has been proposed. This algorithm is based on the…
Cellular Automata (CA) are discrete dynamical systems and an abstract model of parallel computation. The limit set of a cellular automaton is its maximal topological attractor. A well know result, due to Kari, says that all nontrivial…
A cellular automaton is a parallel synchronous computing model, which consists in a juxtaposition of finite automata whose state evolves according to that of their neighbors. It induces a dynamical system on the set of configurations, i.e.…
We introduce a pair of time-reversible models defined on the discrete space-time lattice with 3 states per site, specifically, a vacancy and a particle of two flavours (species). The local update rules reproduce the rule 54 reversible…
State-of-the-art review of cellular automata, cellular automata for partial differential equations, differential equations for cellular automata and pattern formation in biology and engineering.
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…
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…
While for synchronous deterministic cellular automata there is an accepted definition of reversibility, the situation is less clear for asynchronous cellular automata. We first discuss a few possibilities and then investigate what we call…
Causal Graph Dynamics extend Cellular Automata to arbitrary, bounded-degree, time-varying graphs. The whole graph evolves in discrete time steps, and this global evolution is required to have a number of physics-like symmetries:…
The property of reversibility is quite meaningful for the classic theoretical computer science model, cellular automata. For the reversibility problem for a CA under null boundary conditions, while linear rules have been studied a lot, the…
Let A^Z be the Cantor space of bi-infinite sequences in a finite alphabet A, and let sigma be the shift map on A^Z. A `cellular automaton' is a continuous, sigma-commuting self-map Phi of A^Z, and a `Phi-invariant subshift' is a closed,…
This paper proposes a dynamical notion of discrete geodesics, understood as straightest trajectories in discretized curved spacetime. The notion is generic, as it is formulated in terms of a general deviation function, but readily…
In this paper, linear Cellular Automta (CA) rules are recursively generated using a binary tree rooted at "0". Some mathematical results on linear as well as non-linear CA rules are derived. Integers associated with linear CA rules are…
This paper studies directional dynamics in cellular automata, a formalism previously introduced by the third author. The central idea is to study the dynamical behaviour of a cellular automaton through the conjoint action of its global rule…
A general mathematical method is presented for the systematic construction of coupled map lattices (CMLs) out of deterministic cellular automata (CAs). The entire CA rule space is addressed by means of a universal map for CAs that we have…
We study discrete dynamical systems through the topological concepts of limit set, which consists of all points that can be reached arbitrarily late, and asymptotic set, which consists of all adhering values of orbits. In particular, we…
In this paper we introduce a new quantum computation model, the linear quantum cellular automaton. Well-formedness is an essential property for any quantum computing device since it enables us to define the probability of a configuration in…
Classical cellular automata represent a class of explicit discrete spacetime lattice models in which complex large-scale phenomena emerge from simple deterministic rules. With the goal to uncover different physically distinct classes of…