Growth and irreducibility in path-incompressible trees

06/30/2022

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by   George Barmpalias, et al.

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We study effective randomness-preserving transformations of path-incompressible trees. There exists a path-incompressible tree with infinitely many paths, which does not compute any perfect pathwise-random tree. Sparse perfect path-incompressible trees can be effectively densified, almost surely. We characterize the density of branching that pathwise-random trees can have.