Universality in Amorphous Computing

Abstract

Amorphous computer is a theoretical computing model consisting of randomly located tiny devices (called nodes) in some target area. The nodes of an amorphous computer can communicate using short-range radio. The communication radius is small compared to the size of the target area. The nodes are all identical, initially have no identi ers, work asynchronously and there is no standard communication protocol. An amorphous computer must work for any number of nodes under reasonable statistical assumptions concerning the spatial distribution of nodes. Moreover, the computation should use very limited amount of memory on each node. For the just described concept of amorphous computer we investigate the question whether a universal computation is possible at all in a corresponding theoretical model. To answer this question, several subsequent steps are performed. In the rst step, we design a formal minimalist model of a node and of the amorphous computer as a whole. In the second step, we develop communication protocol for the amorphous computer. In the last step, we show the universality by simulating a computation of a universal machine. The size of the amorphous computer will depend on the space complexity of the simulated machine. All the previously mentioned steps are described in detail in this work....