Population Protocols on Graphs: A Hierarchy

  • Olivier Bournez
  • Jonas Lefèvre
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7956)


Population protocols have been introduced as a model in which anonymous finite-state agents stably compute a predicate of the multiset of their inputs via interactions by pairs. In this paper, we consider population protocols acting on families of graphs, that is to say on particular topologies. Stably computable predicates on strings of size n correspond exactly to languages of NSPACE(n), that is to say to non-deterministic space of Turing machines. Stably computable predicates on cliques correspond to semi-linear predicates, namely exactly those definable in Presburger’s arithmetic. Furthermore, we exhibit a strict hierarchy in-between when considering graphs between strings and cliques.


population protocols computability hierarchy space complexity 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Olivier Bournez
    • 1
  • Jonas Lefèvre
    • 1
  1. 1.Ecole Polytechnique, LIXPalaiseau CedexFrance

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