Massively Parallel Automata in Euclidean Space-Time

Denys Duchier (1) , Jérôme Durand-Lose (1) , Maxime Senot (1)

1 LIFO - Laboratoire d'Informatique Fondamentale d'Orléans

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.

Keywords: Model of computation; Abstract geometrical computation; Signal machine; Continuous space-time; Cellular automata; Massive parallelism; Model of computation.

Domains: Computational Complexity [cs.CC]; Logic in Computer Science [cs.LO]

Denys Duchier, Jérôme Durand-Lose, Maxime Senot. Massively Parallel Automata in Euclidean Space-Time. IEEE 4th International Conference on Self-Adaptive and Self-Organizing Systems Workshops (SASOW~'10): Spatial Computing Workshop (SCW '10), 2010, Budapest, Hungary. pp.104-109, ⟨10.1109/SASOW.2010.23⟩. ⟨hal-00511958⟩