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Homonym Population Protocols

  • Olivier BournezEmail author
  • Johanne Cohen
  • Mikaël Rabie
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9466)

Abstract

Angluin et al. introduced Population protocols as a model in which n passively mobile anonymous finite-state agents stably compute a predicate on the multiset of their inputs via interactions by pairs. The model has been extended by Guerraoui and Ruppert to yield the community protocol models where agents have unique identifiers but may only store a finite number of the identifiers they already heard about. The Population protocol model only computes semi-linear predicates, whereas the community protocol model provides the power of a Turing machine with a \(O(n\log n)\) space.

We consider variations on the above models and we obtain a whole landscape that covers and extends already known results. By considering the case of homonyms, that is to say the case when several agents may share the same identifier, we provide a hierarchy that goes from the case of no identifier (population protocol model) to the case of unique identifiers (community protocol model).

We obtain in particular that any Turing Machine on space \(O(\log ^{O(1)} n)\) can be simulated with at least \(O(\log ^{O(1)} n)\) identifiers, a result filling a gap left open in all previous studies.

Our results also extend and revisit in particular the hierarchy provided by Chatzigiannakis et al. on population protocols carrying Turing Machines on limited space, solving the problem of the gap left by this work between per-agent space \(o(\log \log n)\) (proved to be equivalent to population protocols) and \(O(\log n)\) (proved to be equivalent to Turing machines).

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.LIXEcole PolytechniquePalaiseau CedexFrance
  2. 2.LRIUniversité de Paris-SudOrsay CedexFrance

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