# Showing two Turing machines decide different languages

I want to figure out how two languages are different. If we have TM M and TM N, how would I figure out if the languages are different? My intuition is that if a M accepts an input a and N does not then that would prove the languages are different, right?

I'm not too sure if I'm thinking of this correctly.

• You'd have to use something you know about $M$ and $N$ to try to produce a string that's accepted by one and rejected by the other. If all you had was a black box, you wouldn't be able to do anything other than iterate through all strings asking if each one was in the two languages. – David Richerby Mar 14 '17 at 16:41