Reversible parallel computation: An evolving space-model

Lecture Notes in Computer Science

Senot

2012

Abstract. Abstract geometrical computation can solve hard combinatorial problems efficiently: we showed previously how Q-SAT can be solved in bounded space and time using instance-specific signal machines and fractal parallelization. In this article, we propose an approach for constructing a particular generic machine for the same task. This machine deploies the Map/Reduce paradigm over a fractal structure. Moreover our approach is modular : the machine is constructed by combining modules. In this manner, we can easily create generic machines for solving satifiability variants, such as SAT, #SAT, MAX-SAT.

Section: Introductionmentioning

confidence: 99%

Computing in the Fractal Cloud: Modular Generic Solvers for SAT and Q-SAT Variants

Duchier

Lecture Notes in Computer Science

Senot

2012

“…It is inspired by a continuous time and space counterpart of cellular automata emphasizing on the notion of signal which is the key to CA dynamics (Durand-Lose, 2008b) and is somehow related to the approaches of Takeuti (2005) and Hagiya (2005). Geometrically, it is related to the "colored spaces" or "Mondrian spaces" of Jacopini and Sontacchi (1990) which involves polyhedra in Euclidean spaces with a distinguished direction for time. It can also be understood as an idealization of collision computing (Adamatzky, 2002;Adamatzky and Durand-Lose, 2012).…”

Section: Introductionmentioning

confidence: 99%

Abstract geometrical computation 7: geometrical accumulations and computably enumerable real numbers

2012

Nat Comput

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Abstract geometrical computation 7: Geometrical accumulations and computably enumerable real numbersJérôme Durand-Lose To cite this version:Jérôme Durand-Lose. Abstract geometrical computation 7: Geometrical accumulations and computably enumerable real numbers. Natural Computing, Springer Verlag, 2012, 11 (4) Abstract Using rules to automatically extend a drawing on an Euclidean space might lead to accumulating drawings into a single point. Such points are characterized in the context of Abstract geometrical computation.Colored line segments (traces of signals) are drawn according to rules: signals with similar color are parallel and when they intersect, they are replaced according to their colors. Time and space are continuous and accumulations can happen. Constructions exist to unboundedly accelerate a computation and provide, in a finite duration, exact analog values as limits/accumulations.Starting with rational numbers for coordinates and speeds, the time of any isolated accumulation is a c.e. (computably enumerable) real number. There is a signal machine and an initial configuration that accumulates at any c.e. time. Similarly, the spatial positions of isolated accumulations are exactly the d-c.e. (difference of computably enumerable) numbers. Moreover, there is a signal machine that can accumulate at any c.e. time or d-c.e. position depending only on the initial configuration.These existence results rely on a two-level construction: an inner structure simulates a Turing machine that output orders to the outer structure which handles the accumulation. * http://www.univ-orleans.fr/lifo/Members/Jerome.Durand-Lose, Jerome.DurandLose@univ-orleans.fr † This work was partially funded by the ANR project AGAPE, ANR-09-BLAN-0159-03.1

“…Naughton and Woods (2001) presents an optical model manip-ulating continuous images (configurations are elements of {0, 1} R 2 + , but the primitives are also external and their actions non local. Jacopini and Sontacchi (1990) developed an approach where a computation results in a polyhedron. They only encompass finite polyhedron (i.e.…”

Section: Introductionmentioning

confidence: 99%

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

2009

Nat Comput

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.