Yes, but that’s for a functional notion of equivalence—i.e. it’s about whether the two TMs have the same input-output behavior. The notion of equivalence I’m looking at is not just about same input-output, but also structurally-similar computations. Intuitively, I’m asking whether they’re computing the same function in the same way.
(In fact, circumventing the undecidability issue is a key part of why I’m formulating the problem like this in the first place. So you’re definitely asking the right question here.)
Yes, but that’s for a functional notion of equivalence—i.e. it’s about whether the two TMs have the same input-output behavior. The notion of equivalence I’m looking at is not just about same input-output, but also structurally-similar computations. Intuitively, I’m asking whether they’re computing the same function in the same way.
(In fact, circumventing the undecidability issue is a key part of why I’m formulating the problem like this in the first place. So you’re definitely asking the right question here.)