>>12511249Wrong. Collatz conjecture can be formulated in a meaningful way by for example asking to find a proof in ZFC that the statement is true or find a counterexample. It could be that neither is possible, but still it's a valid question to ask.
Meanwhile, asking to find the smallest DFA that distinguishes two strings is way too vague to be meaningful? What if there is no nice description of the DFA or the minimum size?