How Arbitrary is the Representation of a Turing Machine?

Question

Hello all,

I'm working on a related decidability/recognizable problem, and to solve it, I need clarification about the encoding/representation of a turing machine.

I know a turing machine is formally defined as a 7-tuple. If I have a Turing Machine U and another Turing Machine M, is it trivial to design U to recognize some part of M (such as M's alphabet, input symbols, set of accepting states, etc)?

Part of me thinks that because these are finite sets, it's trivial to count over them, but part of me wonders whether or not you can just enumerate some part of M's definition without the possibility of looping into infinity.

Answer 1

Yes, the U stands for the Universal Turing machine. Read about it at http://en.wikipedia.org/wiki/Turing_machine#Universal_Turing_machines.