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I think the article should be rewritten to focus more on [[computable function]]s instead of Turing machines. This should be done in most articles in the computability category. Of course Turing machines are easier to grasp then the abstract concept of computable function, but by focussing on the abstract concept we can eliminate the redundant discussion of [[lamda calculus]], [[recursive function]] and [[Church-Turing thesis]] in each computability article. I guess in many cases the proofs and theorems will get shorter too. We can always add a ''concrete'' example using Turing machines if the article gets to abstract [[User:MathMartin|MathMartin]] 23:59, 9 Nov 2004 (UTC)
:I have the opposite opinion. TM gives very intuitive and simple representation for computability. See the proofs for uncomputability of [[Busy Beaver]] functions. More of the results may be demonstarted on TM (or other programming language) examples. If you get the [[Quine (computing)|Quine]] program, it is easy to expand it to self-explorer program, and then using self-opposite behavior to proof easy non-stoping problem, Godel incompleteness theorem and other results. Such proofs are simple and don't use complex and hard for understanding mathematical notation. [[User:Skelet|Skelet]] 19:16, 7 Dec 2004 (UTC)
::I do not object to using Turing machines as examples, but as with any model, Turing machines only serve to illustrate certain points. Other points can be illustrated better using other models. My point is the main (technical) definition should be based on [[computable function]]s. But at the moment I am not able to devote any amount of time on this topic. So I guess for now things will stay as they are. [[User:MathMartin|MathMartin]] 19:30, 9 Dec 2004 (UTC)
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