  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.
