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Sep 16, 2018 at 23:02 comment added Yuval Filmus My counterexample asks for a sequence of decidable languages $L_1,L_2,\ldots$ such that the language $\{(i,x) : x \in L_i\}$ is not decidable.
Sep 16, 2018 at 18:02 comment added panto I didn't mean that $T$ takes $L$ as input no. Regarding your counter-example question, I guess the issue is that it gives you the ability to solve undecidable problems like the halting problem? (e.g., let $L$ be the unary language where $1^i \in L$ iff $M$ halts on input $x$ where $i$ encodes TM $M$ and input $x$. $L$ can be accepted by non-uniform TMs of course)
Sep 5, 2018 at 6:38 history answered Yuval Filmus CC BY-SA 4.0