On the number of binary-minded individuals required to compute √1/2

We recently obtained partial results on the computational power of population protocols when the population is assumed to be large. We studied in particular a particular protocol that we proved to converge towards 12, using weak-convergence methods for stochastic processes. In this paper, we prove that it is possible to compute 12 with precision >0 in a time polynomial in 1 using a number of agents polynomial in 1, with individuals that can have only two states. This is established through a general result on approximation of stochastic differential equations by a stochastic Euler-like discretization algorithm, of general interest.