On the algebraic numbers computable by some generalized Ehrenfest urns

Marie Albenque (1) , Lucas Gerin (2)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 MODAL'X - Modélisation aléatoire de Paris X

This article deals with some stochastic population protocols, motivated by theoretical aspects of distributed computing. We modelize the problem by a large urn of black and white balls from which at every time unit a fixed number of balls are drawn and their colors are changed according to the number of black balls among them. When the time and the number of balls both tend to infinity the proportion of black balls converges to an algebraic number. We prove that, surprisingly enough, not every algebraic number can be ''computed'' this way.

Keywords: population protocols; distributed computing : approximation of Markov chains; Ehrenfest

Domains: Distributed, Parallel, and Cluster Computing [cs.DC]

Marie Albenque, Lucas Gerin. On the algebraic numbers computable by some generalized Ehrenfest urns. Discrete Mathematics and Theoretical Computer Science, 2012, 14 (2), pp.271-284. ⟨hal-00589621v2⟩