On the Universal Computing Power of Amorphous Computing Systems

  • Authors:
  • Jiří Wiedermann;Lukáš Petrů

  • Affiliations:
  • Academy of Sciences of the Czech Republic, Institute of Computer Science, Pod Vodárenskou věží 2, 182 07, Prague 8, Czech Republic;Charles University, Faculty of Mathematics and Physics, Malostranské náměstí 25, 118 00, Prague 1, Czech Republic

  • Venue:
  • Theory of Computing Systems - Special Issue: Computation and Logic in the Real World; Guest Editors: S. Barry Cooper, Elvira Mayordomo and Andrea Sorbi
  • Year:
  • 2009

Quantified Score

Hi-index 0.00

Visualization

Abstract

Amorphous computing differs from the classical ideas about computations almost in every aspect. The architecture of amorphous computers is random, since they consist of a plethora of identical computational units spread randomly over a given area. Within a limited radius the units can communicate wirelessly with their neighbors via a single-channel radio. We consider a model whose assumptions on the underlying computing and communication abilities are among the weakest possible: all computational units are finite state probabilistic automata working asynchronously, there is no broadcasting collision detection mechanism and no network addresses. We show that under reasonable probabilistic assumptions such amorphous computing systems can possess universal computing power with a high probability. The underlying theory makes use of properties of random graphs and that of probabilistic analysis of algorithms. To the best of our knowledge this is the first result showing the universality of such computing systems.