Massively Parallel Automata in Euclidean Space-Time

Abstract : In the cellular automata (CA) literature, discrete lines in discrete space-time diagrams are often idealized as Euclidean lines in order to design CA or analyze their dynamic behavior. In this paper, we present a parallel model of computation corresponding to this idealization: dimensionless particles move uniformely at fixed velocities along the real line and are transformed when they collide. Like CA, this model is parallel, uniform in space-time and uses local updating. The main difference is the use of the continuity of space and time, which we proceed to illustrate with a construction to solve Q-SAT, the satisfiability problem for quantified boolean formulae, in bounded space and time, and quadratic collision depth.
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Jacob Beal and Olivier Michel and Antoine Spicher. IEEE 4th International Conference on Self-Adaptive and Self-Organizing Systems Workshops (SASOW~'10): Spatial Computing Workshop (SCW '10), 2010, Budapest, Hungary. IEEE Computer Society, pp.104-109, 2010, 〈10.1109/SASOW.2010.23〉
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Denys Duchier, Jérôme Durand-Lose, Maxime Senot. Massively Parallel Automata in Euclidean Space-Time. Jacob Beal and Olivier Michel and Antoine Spicher. IEEE 4th International Conference on Self-Adaptive and Self-Organizing Systems Workshops (SASOW~'10): Spatial Computing Workshop (SCW '10), 2010, Budapest, Hungary. IEEE Computer Society, pp.104-109, 2010, 〈10.1109/SASOW.2010.23〉. 〈hal-00511958〉

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