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We examine the question of solving the extinction probability of a particular class of continuous-time multi-type branching processes, named Markovian binary trees (MBT). The extinction probability is the minimal nonnegative solution of a fixed point equation that turns out to be quadratic, which makes its resolution particularly clear. We analyze first two linear algorithms to compute the extinction probability of an MBT, of which one is new, and, we propose a quadratic algorithm arising fromdoi:10.4230/dagsemproc.07461.9 fatcat:xudvopo7gvbevo4zqyv6jb6b7q