The phase diagram of the coupled sine circle map lattice exhibits a variety of interesting phenomena including spreading regions with spatiotemporal intermittency, non-spreading regions with spatial intermittency, and coherent structures termed solitons. A cellular automaton mapping of the coupled map lattice maps the spreading to non-spreading transition to a transition from a probabilistic to...

The reversibility properties of the elementary cellular automaton with rule number 90 are studied. It is shown that the cellular automaton considered is not reversible when periodic boundary conditions are considered, whereas when null boundary conditions are stated, the reversibility appears when the number of cells of the cellular space is even. The DETGTRI algorithm is used to prove these st...

We study the sizes of minimal finite state machines associated with linear cellular automata. In particular, we construct a class of binary linear cellular automata whose corresponding minimal automata exhibit full exponential blow-up. These cellular automata have Hamming distance 1 to a permutation automaton. Moreover, the corresponding minimal Fischer automata as well as the minimal DFAs have...

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 problem of multidimensional linear cellular automata under boundary conditions. This work proposes a criterion for testing the reversibility of a multidimensio...

We propose the characterization of binary cellular automata using a set of behavioral metrics that are applied to the minimal Boolean form of a cellular automaton’s transition function. These behavioral metrics are formulated to satisfy heuristic criteria derived from elementary cellular automata. Behaviors characterized through these metrics are growth, decrease, chaoticity, and stability. Fro...

Since Richard Feynman introduced the notion of quantum computation in 1982, various models of \quantum computers" have been proposed. These models include quantum Turing machines and quantum circuits. In this paper we deene another quantum computational model, one-dimensional quantum cellular automata, and demonstrate that any quantum Turing machine can be eeciently simulated by a one-dimension...

We discuss cellular automata over arbitrary finitely generated groups. We call a cellular automaton post-surjective if for any pair of asymptotic configurations, every pre-image of one is asymptotic to a pre-image of the other. The well known dual concept is pre-injectivity: a cellular automaton is pre-injective if distinct asymptotic configurations have distinct images. We prove that pre-injec...

The transient behavior of the I-dimensional 2-state 3-input cellular automaton rule 110, one of the simplest "edge of chaos" cellular automata, is investigated numerically. The simulations show that the average transient time Tave increases algebraically with system size N, Tave ~ N"', with a "" 1.08, and that the density of propagating objects (gliders) decays with time as ngl ~ r'Y with I "" ...

Elementary cellular automaton (ECA) rules 9 and 74, members of Chua’s Bernoulli shift rules and Wolfram’s class 2, can generate a host of gliders and complicated glider collisions by introducing the hybrid mechanism. These gliders and collisions are more plentiful than those generated by ECA rule 110. This paper presents a discussion of the symbolic dynamics of the gliders in hybrid cellular au...

Cellular Automata (CA) are discrete, spatially explicit extended dynamic systems. A CA system is composed of adjacent cells or sites arranged as a regular lattice, which evolves in discrete time steps. Each cell is characterized by an internal state whose value belongs to a finite set. The updating of these states is made simultaneously according to a common local transition rule involving only...