When we talk about the enumeration of TM's, do we mean the "regular" deterministic ones? So if we want to enumerate nondeterministic or probabilistic TM's, do we need a separate enumeration?
I can see how we could describe probabilistic TM's as strings, just as we describe the deterministic TM's only now we have two transition functions. Then it also follows that checking whether some string enumerates a probabilistic TM is decidable. Perhaps one could think of a way to create some universal coding of TM's to strings that works for all different kinds of TM's? Perhaps the first ... digits of the enumeration describe what kind of TM (probabilistic, determinstic etc) it is and then follows the description of the TM in the standard fashion. So then we can enumerate all the TM's?
A related question, does a TM know it's own description? Or can we give it that information without loss of generality?
