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I'm having difficulty understanding the proof of the Kleene-Post result. It purports to construct two languages that are not Turing reducible to each other, using a diagonalization argument. I've seen …

(For the below, I referred extensively to this github repo as well as private communication with @aozgaa) Languages can be represented as infinite-length bitstrings (ILB). We will use the two intercha …

Suppose $EQ_\mathrm{TM} \leq_\mathrm{m} \overline{EQ_\mathrm{TM}}$. Then there exists an $f : \Sigma^\star \rightarrow \Sigma^\star$ such that $f(w) \in EQ_\mathrm{TM}$ if and only if $w \in \overline …

Actually, you don't need to construct the DFA, you just need to show that it exists using the Myhill Nerode theorem. Here's how: given a machine $M$ that cannot write on its input, suppose the input h …

Here's a much simpler answer that uses the same idea as @xskxzr's answer. I found the bijection used in that answer not really necessary: it's much simpler to just directly store the number of steps i …