Collision-based computing is an implementation of logical circuits, mathematical machines or other computing and information processing devices in homogeneous uniform unstructured media with traveling mobile localizations. A quanta of information is represented by a compact propagating pattern (glider in cellular automata, soliton in optical system, wave-fragment in excitable chemical system). Logical truth corresponds to presence of the localization, logical false to absence of the localization; logical values can be also represented by a particular state of the localization. When two more or more traveling localizations collide they change their velocity vectors and/or states. Post-collision trajectories and/or states of the localizations represent results of a logical operations implemented by the collision. One of the principle advantages of the a collision-based computing medium-hidden in 1D systems but obvious in 2D and 3D media-is that the medium is architecture-less: nothing is hardwired, there are no stationary wires or gates, a trajectory of a propagating information quanta can be see as a momentary wire. We introduce basics of collision-based computing, and overview the collision-based computing schemes in 1D and 2D cellular automata and continuous excitable media. Also we provide an overview of collision-based schemes where particles/collisions are dimensionless.

geometrical computation 3: Black holes for classical and analog computingJérôme Durand-Lose To cite this version:Jérôme Durand-Lose. The date of receipt and acceptance will be inserted by the editorAbstract The so-called Black Hole model of computation involves a non Euclidean space-time where one device is infinitely "accelerated" on one world-line but can send some limited information to an observer working at "normal pace". The key stone is that after a finite duration, the observer has received the information or knows that no information was ever sent by the device which had an infinite time to complete its computation. This allows to decide semi-decidable problems and clearly falls out of classical computability.A setting in a continuous Euclidean space-time that mimics this is presented. Not only is Zeno effect possible but it is used to unleash the black hole power. Both discrete (classical) computation and analog computation (in the understanding of Blum, Shub and Smale) are considered. Moreover, using nested singularities (which are built), it is shown how to decide higher levels of the corresponding arithmetical hierarchies.Key words Abstract geometrical computation -Analog computationArithmetic hierarchy -Black hole model -Malament-Hogarth space-time -Hyper-computing -Zeno phenomenon Disclaimer The author is a computer scientist and not a physicist. So that it is refereed to other contributions in this issue and to the cited bibliography for enlightenment on black holes. The present article aims at providing a context of computation exhibiting the same computing capabilities as black holes and at illustrating the point of view of a computer scientist.

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