262 research outputs found
On the injectivity of the global function of a cellular automaton in the hyperbolic plane (extended abstract)
In this paper, we look at the following question. We consider cellular
automata in the hyperbolic plane, (see Margenstern, 2000, 2007 and Margenstern,
Morita, 2001) and we consider the global function defined on all possible
configurations. Is the injectivity of this function undecidable? The problem
was answered positively in the case of the Euclidean plane by Jarkko Kari, in
1994. In the present paper, we show that the answer is also positive for the
hyperbolic plane: the problem is undecidable
The Game of Life on the Hyperbolic Plane
In this paper, we work on the Game of Life on the hyperbolic plane. We are interested in different tessellations on the hyperbolic plane and different Game of Life rules. First, we show the exponential growth of polygons on the pentagon tessellation. Moreover, we find that the Group of 3 can keep the boundary of a set not getting smaller. We generalize the existence of still lifes by computer simulations. Also, we will prove some propositions of still lifes and cycles. There exists a still life under rules B1, B2, and S3
Computing in the fractal cloud: modular generic solvers for SAT and Q-SAT variants
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
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