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

Encyclopedia of Complexity and Systems Science

Ergodic theory

Around probabilistic cellular automata

Dynamical behavior of additive cellular automata over finite abelian groups

The asymptotic behaviour of a cellular automaton iterated on a random configuration is well described by
its limit probability measure(s). In this paper, we characterise measures and sets of measures that can be reached as
limit points after iterating a cellular automaton on a simple initial measure. 
In addition to classical topological constraints, we exhibit necessary computational obstructions. With an additional
hypothesis of connectivity, we show these computability conditions are sufficient by constructing a cellular automaton
realising these sets, using auxiliary states in order to perform computations. Adapting this construction, we obtain a
similar characterisation for the Ces\`aro mean convergence, a Rice theorem on the sets of limit points, and we are able
to perform computation on the set of measures, i.e. the cellular automaton converges towards a set of limit points that
depends on the initial measure. Last, under non-surjective hypotheses, it is possible to remove auxiliary states from
the construction.

https://hal.archives-ouvertes.fr/hal-01299001/document

Characterisation of sets of limit measures of a cellular automaton iterated on a random configuration

The asymptotic behavior of a cellular automaton iterated on a random configuration is well described by its limit probability measure(s). In this paper, we characterize measures and sets of measures that can be reached as limit points after iterating a cellular automaton on a simple initial measure, in the same spirit as SRB measures. In addition to classical topological constraints, we exhibit necessary computational obstructions. With an additional hypothesis of connectivity, we show these computability conditions are sufficient by constructing a cellular automaton realising these sets, using auxiliary states in order to perform computations. Adapting this construction, we obtain a similar characterization for the Cesaro mean convergence, a Rice theorem on the sets of limit points, and we are able to perform computation on the set of measures, i.e. the cellular automaton converges towards a set of limit points that depends on the initial measure. Last, under non-surjective hypotheses, it is possible to remove auxiliary states from the construction.

Characterisation of sets of limit measures after iteration of a cellular automaton on an initial measure

L'objet de cette these est l'etude de l'auto-organisation dans les automates cellulaires unidimensionnels.Les automates cellulaires sont un systeme dynamique discret ainsi qu'un modele de calcul massivement parallele, ces deux aspects s'influencant mutuellement. L'auto-organisation est un phenomene ou un comportement organise est observe asymptotiquement, independamment de la configuration initiale. Typiquement, nous considerons que le point initial est tire aleatoirement: etant donnee une mesure de probabilite decrivant une distribution de configurations initiales, nous etudions son evolution sous l'action de l'automate, le comportement asymptotique etant decrit par la(les) mesure(s) limite(s).Notre etude presente deux aspects. D'abord, nous caracterisons les mesures qui peuvent etre atteintes a la limite par les automates cellulaires; ceci correspond aux differents comportements asymptotiques pouvant apparaitre en simulation. Cette approche rejoint divers resultats recents caracterisant des parametres de systemes dynamiques par des conditions de calculabilite, utilisant des outils d'analyse calculable. Il s'agit egalement d'une description de la puissance de calcul des automates cellulaires sur les mesures.Ensuite, nous proposons des outils pour letude de l'auto-organisation dans des classes restreintes. Nous introduisons un cadre d'etude d'automates pouvant etre vus comme un ensemble de particules en interaction, afin d'en deduire des proprietes sur leur comportement asymptotique. Une derniere direction de recherche concerne les automates convergeant vers la mesure uniforme sur une large classe de mesures initiales (phenomene de randomisation).

Asymptotic behaviour of cellular automata : computation and randomness

For some classes of cellular automata, we observe empirically a phenomenon of self-organization: starting from a random configuration, regular strips separated by defects appear in the space-time diagram. When there is no creation of defects, all defects have the same direction after some time. In this article, we propose to formalise this phenomenon. Starting from the notion of propagation of defect by a cellular automaton formalized in [Piv07b, Piv07a], we show that, when iterating the automaton on a random configuration, defects in one direction only remain asymptotically.

/pdf/self-organization-in-cellular-automata-a-particle-based-2o3043g6bu.pdf

Self-organization in cellular automata: a particle-based approach

We study the difficulty of computing topological entropy of subshifts subjected to mixing restrictions. This problem is well-studied for multidimen
sional subshifts of finite type: there exists a threshold in the irreducibility rate where the difficulty jumps from computable to uncomputable, but its location is an open problem. In this paper, we establish the location of this threshold for a more general class, subshifts with decidable languages, in any dimension.

Benjamin Hellouin de Menibus

Papers

Characterisation of sets of limit measures of a cellular automaton iterated on a random configuration

Characterisation of sets of limit measures after iteration of a cellular automaton on an initial measure

Asymptotic behaviour of cellular automata : computation and randomness

Self-organization in cellular automata: a particle-based approach

Effect of quantified irreducibility on the computability of subshift entropy