Definition talk:Turing Machine

I've seen definitions like the one here in a few books, and it gets across the idea, but we might additionally want a more formal definition on this page that matches up with the description here. I'm bringing this up because the new Existence_of_Uncomputable_Functions page's proof is apparently hoping to link to a result that will essentially be a redefinition of Turing Machines that makes that proof easier.

So, question: do we want a formal definition on this page, or (in view of the fact that there's lots of things which are essentially equivalent to turing machines and could be called by the same name) do we want to have separate pages formally defining objects and justifying using them when we say "Turing machine" by verifying that they fit the informal description here?

Also, I feel like I should question the use of the word "algorithm(ic)" in the definition of a Turing machine (even informal), since part of the point of studying them is to get a formalized idea and understanding of algorithms. :D

-- Qedetc 17:57, 15 June 2011 (CDT)


 * Be a nice-to-have, perhaps (in that it leads us to the concept of "Turing-complete" computer languages (or whatever that malarkey is all about) but we already have a fairly comprehensive analysis of computability from the point of view of an Unlimited Register Machine. All we need to do is prove that a URM can be emulated by a Turing machine and we've done all we need. I do not think it's worth recreating the entire sequence of results from the point of view of a TM.
 * Besides, that Existence of Uncomputable Functions page has already been deleted. --prime mover 00:16, 16 June 2011 (CDT)


 * Ah, I see. I hadn't poked around much.  With all the register machine stuff here it definitely seems like it would (if nothing else) be an inefficient way to spend time if one were to redo it all with Turing machines. -- Qedetc 00:41, 16 June 2011 (CDT)