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.

No abstract

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.

No abstract