On the convergence of population protocols when population goes to infinity

Olivier Bournez (1) , Philippe Chassaing (2) , Xavier Koegler , Lucas Gerin (2) , Johanne Cohen (3)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 IECN - Institut Élie Cartan de Nancy
3 PRISM - Parallélisme, Réseaux, Systèmes, Modélisation

Population protocols have been introduced as a model of sensor networks consisting of very limited mobile agents with no control over their own movement. A population proto- col corresponds to a collection of anonymous agents, modeled by finite automata, that interact with one another to carry out computations, by updating their states, using some rules. Their computational power has been investigated under several hypotheses but always when restricted to finite size populations. In particular, predicates stably computable in the original model have been characterized as those definable in Presburger arithmetic. We study mathematically the convergence of population protocols when the size of the population goes to infinity. We do so by giving general results, that we illustrate through the example of a particular population protocol for which we even obtain an asymptotic development. This example shows in particular that these protocols seem to have a rather different computational power when a huge population hypothesis is considered.

Mots clés: Population protocols; Computability; Limits

Domaines: Informatique et théorie des jeux [cs.GT]

Olivier Bournez, Philippe Chassaing, Xavier Koegler, Lucas Gerin, Johanne Cohen. On the convergence of population protocols when population goes to infinity. Applied Mathematics and Computation, 2009, Applied Mathematics and Computation, 215, pp.1340-1350. ⟨10.1016/j.amc.2009.04.056⟩. ⟨inria-00432318⟩