Every organisation from the scale of whole countries down to small companies has a list of system developments which have ended in various forms of disaster. The nature of the failures varies but typical examples are: cost overruns; timescale overruns and sometimes, loss of life. The post-mortems to these systems reveal a wide range of reasons all the way from hardware failures, through software errors right to major system level mistakes. More importantly a large number of these systems share one attribute: complexity. This paper presents a fresh look at the nature of complexity in the building of computer based systems.

http://ieeexplore.ieee.org/iel3/4458/12639/00581896.pdf

Complex systems

https://www.ibisc.univ-evry.fr/~hutzler/Cours/IMBI_MPS/Kari05.pdf

Theory of cellular automata: a survey

The Li–Yorke definition of chaos proved its value for interval maps. In this paper it is considered in the setting of general topological dynamics. We adopt two opposite points of view. On the one hand sufficient conditions for Li–Yorke chaos in a topological dynamical system are given. We solve a long–standing open question by proving that positive entropy implies Li–Yorke chaos. On the other hand properties of dynamical systems without Li–Yorke pairs are investigated; in addition to having entropy 0, they are minimal when transitive, and the property is stable under factor maps, arbitrary products and inverse limits. Finally it is proved that minimal systems without Li–Yorke pairs are disjoint from scattering systems.

On li-yorke pairs

Cellular automata are simple models of computation which exhibit fascinatingly complex behavior. They have captured the attention of several generations of researchers, leading to an extensive body of work. Here we trace a history of cellular automata from their beginnings with von Neumann to the present day. The emphasis is mainly on topics closer to computer science and mathematics rather than physics, biology or other applications. The work should be of interest to both new entrants into the field as well as researchers working on particular aspects of cellular automata.

http://krchowdhary.com/me-tfl/0-a%20brief%20history%20of%20cellular%20automata.pdf

A brief history of cellular automata

Cellular Automata.- Residually Finite Groups.- Surjunctive Groups.- Amenable Groups.- The Garden of Eden Theorem.- Finitely Generated Amenable Groups.- Local Embeddability and Sofic Groups.- Linear Cellular Automata.- Nets and the Tychonoff Product Theorem.- Uniform Structures.- Symmetric Groups.- Free Groups.- Inductive Limits and Projective Limits of Groups.- The Banach-Alaoglu Theorem.- The Markov-Kakutani Fixed Point Theorem.- The Hall Harem Theorem.- Complements of Functional Analysis.- Ultrafilters.

Cellular Automata and Groups

— A cover of some compact set X by two non dense open sets is called a standard cover. In the cartesian square of a flow (X, T ), pairs (x, x′) outside the diagonal are defined as entropy pairs whenever any standard cover (U, V ) such that (x, x′) ∈ Int(Uc) × Int(V c) has positive entropy. The set of such pairs is nonempty provided h(X, T ) > 0 ; it is T × T -invariant, and all pairs in its closure belong either to it or to the diagonal. A flow is said to have uniform positive entropy if any standard cover has positive entropy (or if all non diagonal pairs are entropy pairs). Properties of entropy pairs are used to show that flows with uniform positive entropy (in fact a wider class) are disjoint from minimal flows with entropy 0. A flow with uniform positive entropy containing only one periodic orbit is constructed. (*) Texte recu le 10 mars 1992. F. BLANCHARD, Laboratoire de Mathematiques Discretes, case 930, 163 av. de Luminy, 13288 Marseille Cedex 09 (France). e-mail : blanchar@lmd.univ-mrs.fr. AMS classification : 54H20. BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE 0037–9484/1993/465/$ 5.00 c © Societe mathematique de France

/pdf/a-disjointness-theorem-involving-topological-entropy-179obrihzc.pdf

A disjointness theorem involving topological entropy

To every one-sided one-dimensional cellular automatonF with neighbourhood radiusr we associate its canonical factor defined by considering only the firstr coordinates of all the images of points under the powers ofF. Whenever the cellular automaton is surjective, this factor is a subshift which plays a primary role in its dynamics. In this article we study the class of positively expansive one-sided cellular automata, i.e. those that are conjugate to their canonical factors. This class is a natural generalisation of the toggle or permutative cellular automata introduced in [He]. We prove that the canonical factors of positively expansive one-sided cellular automata are mixing subshifts of finite type that are shift equivalent to full shifts. Moreover, the uniform Bernoulli measure is the unique measure of maximal entropy forF. Consequently, their natural extensions are Bernoulli. We also describe a family of non-permutative positively expansive cellular automata.

Dynamical properties of expansive one-sided cellular automata

The Besicovitch and Weyl pseudometrics on the space AŸ of biinfinite sequences measure the density of differences in either the central or arbitrary segments of given sequences. The Besicovitch and Weyl spaces are obtained from A by factoring through the equivalence of zero distance. Cellular automata are considered as dynamical systems on the Besicovitch and Weyl spaces and their topological and dynamical properties are compared with those they possess in the Cantor space.

François Blanchard

Papers

On li-yorke pairs

A disjointness theorem involving topological entropy

Dynamical properties of expansive one-sided cellular automata

Cellular Automata in the Cantor, Besicovitch, and Weyl Topological Spaces

Topological and measure-theoretic properties of one-dimensional cellular automata