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May 15, 2021 at 14:29 comment added Yuval Filmus I gave you enough hints.
May 15, 2021 at 14:29 comment added vesii For the first part: how to prove that if $f(x)=1$ then $x\in \Sigma^*$ iff $f(x)\in HP$?
May 15, 2021 at 13:26 history answered Yuval Filmus CC BY-SA 4.0