A Simple n-Dimensional Intrinsically Universal Quantum Cellular Automaton

We describe a simple n-dimensional quantum cellular automaton (QCA) capable of simulating all others, in that the initial configuration and the forward evolution of any n-dimensional QCA can be encoded within the initial configuration of the intrinsically universal QCA. Several steps of the intrinsically universal QCA then correspond to one step of the simulated QCA. The simulation preserves the topology in the sense that each cell of the simulated QCA is encoded as a group of adjacent cells in the universal QCA.Comment: 13 pages, 7 figures. In Proceedings of the 4th International Conference on Language and Automata Theory and Applications (LATA 2010), Lecture Notes in Computer Science (LNCS). Journal version: arXiv:0907.382

Characterizing asymptotic randomization in abelian cellular automata

Abelian cellular automata (CAs) are CAs which are group endomorphisms of the full group shift when endowing the alphabet with an abelian group structure. A CA randomizes an initial probability measure if its iterated images have weak*-convergence towards the uniform Bernoulli measure (the Haar measure in this setting). We are interested in structural phenomena, i.e., randomization for a wide class of initial measures (under some mixing hypotheses). First, we prove that an abelian CA randomizes in Cesaro mean if and only if it has no soliton, i.e., a non-zero finite configuration whose time evolution remains bounded in space. This characterization generalizes previously known sufficient conditions for abelian CAs with scalar or commuting coefficients. Second, we exhibit examples of strong randomizers, i.e., abelian CAs randomizing in simple convergence; this is the first proof of this behaviour to our knowledge. We show, however, that no CA with commuting coefficients can be strongly randomizing. Finally, we show that some abelian CAs achieve partial randomization without being randomizing: the distribution of short finite words tends to the uniform distribution up to some threshold, but this convergence fails for larger words. Again this phenomenon cannot happen for abelian CAs with commuting coefficients.Basal project, Universidad de Chile: PFB-03 CM

µ-Limit Sets of Cellular Automata from a Computational Complexity Perspective

This paper is about µ-limit sets of cellular automata, i.e. sets of configurations made of words which have a positive probability to appear arbitrarily late in the evolution, starting from an initial µ-random configuration. More precisely, we investigate the computational complexity of these sets and of decision problems concerning them. Our main results are: first, that such a set can have a Σ 0 3-hard language, second that it can contain only α-complex configurations and third that any non-trivial property concerning these sets is at least Π 0 3-hard. We also prove various complexity upper bounds, study some restriction of these questions to particular classes of cellular automata, and study different types of (non-)convergence of the probability of appearance of a word in the evolution

New methodological approach to morphological kinetics

The way of characterizing an interfacial morphology and its relation to the mechanism of transformation of a solid are discussed in this paper for the particular case of electrochemical dissolution. Several parameters, useful in the description of the morphology and its variation with time, are proposed. Moreover, a physical model and its mathematical formulation are developed in order to predict the morphological changes of the interface. The results of numerical and analytical solutions to this problem are compared with experimental data obtained for two cases: aqueous corrosion of copper and electrolytic polishing of a stainless steel

Bulking I: an Abstract Theory of Bulking ⋆

International audienceThis paper is the first part of a series of two papers dealing with bulking: a quasi-order on cellular automata comparing space-time diagrams up to some rescaling. Bulking is a generalization of grouping taking into account universality phenomena, giving rise to a maximal equivalence class. In the present paper, we discuss the proper components of grouping and study the most general extensions. We identify the most general space-time transforms and give an axiomatization of bulking quasi-order. Finally, we study some properties of intrinsically universal cellular automata obtained by comparing grouping to bulking