suspect $L_2$ is more subtle than that. if you have a TM that recognizes a regular language, how do you extract the DFA from that TM? suspect that could be hard or undecidable....? imagine for example the TM takes a very long time to accept or reject some words etc? thinking out loud... it is computable if there is a time or space limit, but otherwise, suspect it is uncomputable. this might be a g