A model of an amorphous computer and its communication protocol

Abstract

We design a formal model of an amorphous computer suitable for theoretical investigation of its computational properties. The model consists of a finite set of nodes created by RAMs with restricted memory, which are dispersed uniformly in a given area. Within a limited radius the nodes can communicate with their neighbors via a single-channel radio. The assumptions on low-level communication abilities are among the weakest possible: the nodes work asynchronously, there is no broadcasting collision detection mechanism and no network addresses. For the underlying network we design a randomized communication protocol and analyze its efficiency. The subsequent experiments and combinatorial analysis of random networks show that the expectations under which our protocol was designed are met by the vast majority of the instances of our amorphous computer model. © Springer-Verlag Berlin Heidelberg 2007.