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Non-deterministic Population Protocols

  • Joffroy Beauquier
  • Janna Burman
  • Laurent Rosaz
  • Brigitte Rozoy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7702)

Abstract

In this paper we show that, in terms of generated output languages, non-deterministic population protocols are strictly more powerful than deterministic ones. Analyzing the reason for this negative result, we propose two slightly enhanced models, in which non-deterministic population protocols can be exactly simulated by deterministic ones. First, we consider a model in which interactions are not only between couples of agents, but also between triples and in which non-uniform initial states are allowed. We generalize this transformation and we prove a general property for a model with interactions between any number of agents. Second, we simulate any non-deterministic population protocol by a deterministic one in a model where a configuration can have an empty output.

Non-deterministic and deterministic population protocols are then compared in terms of inclusion of their output languages, that is, in terms of solvability of problems. We present a transformation realizing this inclusion. It uses (again) the natural model with interactions of triples, but does not need non-uniform initial states. As before, this result is generalized for the natural model with interactions between any number of agents.

Note that the transformations in the paper apply to a whole class of non-deterministic population protocols (for a proposed model), in contrast with the transformations proposed in previous works, which apply only to a specific sub-class of protocols (satisfying a so called “elasticity” condition).

Keywords

Mobile Agent Output Sequence Population Protocol Deterministic Rule Presburger Arithmetic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Joffroy Beauquier
    • 1
    • 2
  • Janna Burman
    • 1
    • 2
  • Laurent Rosaz
    • 1
  • Brigitte Rozoy
    • 1
    • 2
  1. 1.LRIUniversité Paris Sud XIFrance
  2. 2.Grand Large projectINRIA Saclay - Ile de FranceFrance

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