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Cellular Automata (CA), as they are presented in the literature, are abstract mathematical models of computation. In this pa- per we present an alternate approach: using the CA as a model or theory of physical systems and devices. While…
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…
Hochman asked whether there exists a cellular automaton $F$ such that every cellular automaton is a factor of $F$ in the dynamical sense. In particular, we do not require the factor map to commute with the spatial shifts. We show that no…
We show that a partially hyperbolic system can have at most a finite number of compact center-stable submanifolds. We also give sufficient conditions for these submanifolds to exist and consider the question of whether they can intersect…
Cellular automata are arrays of finite state machines that can exist in a finite number of states. These machines update their states simultaneously based on specific local rules that govern their interactions. This framework provides a…
We propose a simple cellular automaton model of a self-healing system and investigate its properties. In the model, the substrate is a two-dimensional checkerboard configuration which can be damaged by changing values of a finite number of…
The emergence of complex behaviors in cellular automata is an area that has been widely developed in recent years with the intention to generate and analyze automata that produce space-moving patterns or gliders that interact in a periodic…
While the reversibility of multidimensional cellular automata is undecidable and there exists a criterion for determining if a multidimensional linear cellular automaton is reversible, there are only a few results about the reversibility…
We show how to construct a deterministic nearest-neighbour cellular automaton (CA) with four states which emulates diffusion on a one-dimensional lattice. The pseudo-random numbers needed for directing random walkers in the diffusion…
Cellular automata are one-dimensional arrays of interconnected interacting finite automata. We investigate one of the weakest classes, the real-time one-way cellular automata, and impose an additional restriction on their inter-cell…
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…
A natural architecture for nanoscale quantum computation is that of a quantum cellular automaton. Motivated by this observation, in this paper we begin an investigation of exactly unitary cellular automata. After proving that there can be…
Cellular Automata have been used since their introduction as a discrete tool of modelization. In many of the physical processes one may modelize thus (such as bootstrap percolation, forest fire or epidemic propagation models, life without…
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,…
We present a Fermionic Cellular Automaton model which describes massless Dirac fermion in 1+1 dimension coupled with local, number preserving interaction. The diagonalization of the two particle sector shows that specific values of the…
If a cellular automaton (CA) is started with a single ON cell, how many cells will be ON after n generations? For certain "odd-rule" CAs, including Rule 150, Rule 614, and Fredkin's Replicator, the answer can be found by using the…
We present a preliminary study of a new class of two-input cellular automata called eventually number-conserving cellular automata characterized by the property of evolving after a finite number of time steps to states whose number of…
We investigate how increasing the dimension of the array can help to draw signals on cellular automata.We show the existence of a gap of constructible signals in any dimension. We exhibit two cellular automata in dimension 2 to show that…
One-dimensional cellular automata are discrete dynamical systems that operate on an infinite lattice of sites and are characterized by the locality and uniformity of their update rule. Permutations of the state set and isometric…
In this work we provide analytic results of infinite one-dimensional cellular automaton(CA). By realizing symbolic products, we investigate a subclass of infinite CA and prove analytically that within this subclass the only allowed…