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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…
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…
A two-dimensional finite automaton has a read-only input head that moves in four directions on a finite array of cells labelled by symbols of the input alphabet. A three-way two-dimensional automaton is prohibited from making upward moves,…
We study the dynamics of the Rule 150 reversible cellular automaton (RCA). This is a one-dimensional lattice system of binary variables with synchronous (Floquet) dynamics, corresponding to a bulk deterministic and reversible discrete…
A novel two-state, Reversible Cellular Automata (RCA) is described. This three-dimensional RCA is shown to be capable of universal computation. Additionally, evidence is offered that this RCA Is capable of universal construction.
This paper presents a classification of Cellular Automata rules based on its properties at the nth iteration. Elaborate computer program has been designed to get the nth iteration for arbitrary 1-D or 2-D CA rules. Studies indicate that the…
Cellular automata are a set of computational models in discrete space that have a discrete time evolution defined by neighbourhood rules. They are used to simulate many complex systems in physics and science in general. In this work,…
There exists an index theory to classify strictly local quantum cellular automata in one dimension. We consider two classification questions. First, we study to what extent this index theory can be applied in higher dimensions via…
Recently Prosen and Mej\'ia-Monasterio (J. Phys. A: Math. Theor. 49 (2016) 185003) obtained exact nonequilibrium steady states of an integrable and reversible cellular automaton driven by some stochastic boundary conditions. In this paper,…
This paper investigates the time-bounded version of the reachability problem for hybrid automata. This problem asks whether a given hybrid automaton can reach a given target location within T time units, where T is a constant rational…
For the first time a mathematical object is presented - a reversible cellular Automaton - with many paradoxical qualities, the main ones among them are: a frequent quickly return to its original state, the presence of a large number of…
Periodicity and relaxation are investigated for the trajectories of the states in one-dimensional finite cellular automata with rule-90 and 150. The time evolutions are described with matrices. Eigenvalue analysis is applied to clarify the…
This tutorial is about cellular automata that exhibit 'cold dynamics'. By this we mean zero entropy, stabilization of all orbits, trivial asymptotic dynamics, etc. These are purely transient irreversible dynamics, but they capture many…
Probing the ability of automata networks to solve decision problems has received a continuous attention in the literature, and specially with the automata reaching the answer by distributed consensus, i.e., their all taking on a same state,…
A probabilistic cellular automaton for cargo transport is presented that generalizes the totally asymmetric exclusion process with a defect from continuous time to parallel dynamics. It appears as an underlying principle in cellular…
Cellular automata are often used to model systems in physics, social sciences, biology that are inherently asynchronous. Over the past 20 years, studies have demonstrated that the behavior of cellular automata drastically changed under…
A condition characterizing the class of regular languages which have several nonisomorphic minimal reversible automata is presented. The condition concerns the structure of the minimum automaton accepting the language under consideration.…
Controllability, one of the fundamental concepts in control theory, consists in guiding a system from an initial state to a desired one within a limited (and possibly minimum) time interval. When the objective is limited to a specific…
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 extend the usual definition of cellular automaton on a group in order to deal with a new kind of cellular automata, like cellular automata in the hyperbolic plane and we explore some properties of these cellular automata. This definition…