On Lipschitz Bijections Between Boolean Functions

@article{Rao2017OnLB,
  title={On Lipschitz Bijections Between Boolean Functions},
  author={Shravas Rao and Igor Shinkar},
  journal={Combinatorics, Probability and Computing},
  year={2017},
  volume={27},
  pages={411 - 426}
}
Given two functions f,g : {0,1}n → {0,1}, a mapping ψ : {0,1}n → {0,1}n is said to be a mapping from f to g if it is a bijection and f(z) = g(ψ(z)) for every z ∈ {0,1}n. In this paper we study Lipschitz mappings between Boolean functions. Our first result gives a construction of a C-Lipschitz mapping from the Majority function to the Dictator function for some universal constant C. On the other hand, there is no n/2-Lipschitz mapping in the other direction, namely from the Dictator function to… 

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