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On the Universal Computing Power of Amorphous Computing Systems

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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 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.

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Authors and Affiliations

  1. Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodárenskou věží 2, 182 07, Prague 8, Czech Republic

    Jiří Wiedermann

  2. Faculty of Mathematics and Physics, Charles University, Malostranské náměstí 25, 118 00, Prague 1, Czech Republic

    Lukáš Petrů

Authors
  1. Jiří Wiedermann
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  2. Lukáš Petrů
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Correspondence to Jiří Wiedermann.

Additional information

This research was carried out within the institutional research plan AV0Z10300504 and partially supported by the GA ČR grant No. 1ET100300517 and GD201/05/H014. A preliminary, shorter version of this paper has been presented at the Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 2007 and published in the proceedings from this conference.

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Wiedermann, J., Petrů, L. On the Universal Computing Power of Amorphous Computing Systems. Theory Comput Syst 45, 995–1010 (2009). https://doi.org/10.1007/s00224-009-9178-6

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  • DOI: https://doi.org/10.1007/s00224-009-9178-6

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