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 with computable oracle-use. Sparse perfect path-incompressible trees can be effectively densified, almost surely. We characterize the branching density of path-random trees.

翻译：我们研究了路径不可压缩树的有效随机性保持变换。部分具有无穷多路径的路径不可压缩树无法通过可计算预言机使用计算出完美路径随机树。稀疏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。