Computability in Amorphous Structures

  • Authors:
  • Jiří Wiedermann;Lukáš Petru

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

  • Venue:
  • CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
  • Year:
  • 2007

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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 non-uniform families of such amorphous computers can possess universal computing power with a high probability. To the best of our knowledge this is the first result showing the universality of such computing systems.