L = {T | T is a turing machine that recognizes {00, 01}} Prove L is undecidable

Question

L = {<T> | T is a turing machine that recognizes {00, 01}}

Prove L is undecidable.

I am really having difficulties even understanding the reduction to use here.

I'm not asking for free lunch, just a push in the right direction.

Answer 1

A direct application of Rice's theorem will let you prove this without doing any work at all.

Some Turing machines recognize {00, 01}. Some don't. The difference is semantic in that it has to do with the strings accepted, not the structure of the automaton. Hence, by Rice's theorem, this set is undecidable.