Abstract geometrical computation 3: Black holes for classical and analog computing

Jérôme Durand-Lose (1)

1 LIFO - Laboratoire d'Informatique Fondamentale d'Orléans

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.

Mots clés: Abstract geometrical computation; Analog computation; Arithmetic hierarchy; Black hole model; Malament-Hogarth space-time; Hyper-computing; Zeno phenomenon

Domaines: Logique en informatique [cs.LO]; Autre [cs.OH]

Jérôme Durand-Lose. Abstract geometrical computation 3: Black holes for classical and analog computing. Natural Computing, 2009, 8 (3), pp.455-472. ⟨10.1007/s11047-009-9117-0⟩. ⟨hal-00447966⟩