We study effective randomness-preserving transformations of path-incompressible trees. Some path-incompressible trees with infinitely many paths do not compute perfect path-random trees. Sparse perfect path-incompressible trees can be effectively densified, almost surely. We characterize the branching density of path-random trees.

翻译：我们研究路径不可压缩树的有效随机性保持变换。一些具有无穷多条路径的路径不可压缩树无法计算完美的路径随机树。稀疏的完美路径不可压缩树几乎必然可以被有效稠密化。我们刻画了路径随机树的分支密度。