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Lipschitz bijections between boolean functions
We answer four questions from a recent paper of Rao and Shinkar on Lipschitz
bijections between functions from to . (1) We show that
there is no -bi-Lipschitz bijection from to
such that each output bit depends on input bits. (2) We
give a construction for a mapping from to
which has average stretch , matching a previously known lower
bound. (3) We give a 3-Lipschitz embedding such that for
all . (4) We show that with high probability there is a
-bi-Lipschitz mapping from to a uniformly random
balanced function
- β¦