Talk:Computability theory (computer science)

message: I think the article should be rewritten to focus more on computable functions 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 MathMartin 23:59, 9 Nov 2004 (UTC)
replies: text: 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 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. Skelet 19:16, 7 Dec 2004 (UTC)
replies: text: 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 functions. 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. MathMartin 19:30, 9 Dec 2004 (UTC)
thread_title: Refocus article on Computable functions

message: As far as I remember (and correct me if I am wrong), this article used to have a lot of content. Now it is just 8 lines. Computability theory deserves more than just a short definition and two links. This is an ENCYCLOPEDIA, not a DICTIONARY. Who destroyed the old content?! ---- David 
November 13, 2005
: Yes, this is indeed very strange! I do not know the previous article, but this topic cannot possibly be that short after 4 years of Wikipedia! Hints on what might have happened here are found at the deleted changes page. There it says that "00:11, 26 October 2005 Timwi deleted "Computability theory" (Deleted to make way for move)" Yet, I do not understand it. What moved? Where did it move to? I will go and ask Timwi. --Markus Krötzsch 21:05, 15 November 2005 (UTC)
thread_title:  What happened to this article?! 

message: It's become trendy in recent years, due to the influence of Robert I. Soare, to use the term "computability theory" to refer to what's traditionally called "recursion theory", and in fact recursion theory is a redirect here. However this article is not much about recursion theory (Turing degrees, effective descriptive set theory, that sort of thing), but more about models of in-principle-physically-realizable computation. Recursion theory is a branch of math logic, not of theory of computation.
So what do we do about this? I see there's a merge template to merge to computation. For most of the content in the current article that's probably fine. But there should also be an article about what math-logicians call computability theory or recursion theory. Perhaps we need a dab page under the name computability theory. --Trovatore 04:26, 26 November 2005 (UTC)
replies: text: This article should be moved to theory of computation (which I can't do because I'm not an admin). This should be made in to a disambig to theory of computation and a to be written recursion theory. —R. Koot 04:40, 26 November 2005 (UTC)
replies: text: So I've taken an awkward first step, moving the article to Computability theory (computation), which I don't propose as the permanent name, but just a good place to put this content while we sort things out. Some of the content does need to be reproduced in the (new stub) recursion theory article.  Roughly speaking, recursion theory starts with what is here called "Unreasonable models of computation". Definitely the halting problem needs to be mentioned in the "recursion theory" article. --Trovatore 05:22, 26 November 2005 (UTC)
thread_title: Problematic name

message: Some time ago I proposed splitting out recursion theory as a separate article and renaming this content to computability theory (computer science). I now think that was a mistake. I felt that non-computer-science topics were being given short shrift in the article. It now seems to me that all research topics are given short shrift.
The exposition of the elementary material is too slow, and there's not enough outline of more advanced material. The tasks of defining what it means to be computable, and establishing that there are things that aren't computable, should be described briefly, with links to computable function and Turing machine for more details. Then there should be a series of sections, one for each identifiable theme within computability theory, with a blurb on each and a link to a more-detailed main article. Themes that come to mind are complexity theory (P vs NP, PSPACE, hierarchies, etc), structure of the Turing degrees, randomness (the sort of stuff Rod Downey and his former students do), and effective descriptive set theory; computer scientists may have others they want to add. --Trovatore 16:09, 8 February 2006 (UTC)
replies: text: I think this might be a good idea as it does appear to be the same subject, only that computer scientists and mathematical logicians have a different focus (e.g. computer scientists start with the work of Turing and Church and stop at Oracle machines, while mathematical logians start with the work of Kleene and focus on Oracle machines and beyond). —Ruud 16:54, 8 February 2006 (UTC)
replies: text: Well, so that was more or less what I was thinking back at the time of the split (in fact, I think I wrote something very much like it) but now I'm not so sure. It seems to me that mathematical logicians are interested in, say P and NP and related hierarchies (which are all solidly within "computable"), and computer scientists are interested in random sequences, even though they can't be computable. So while there's a difference in focus, there's no clear borderline. I just think the article spends too much time on computable-vs-not-computable, which is pretty cut and dried and kind of boring. We know what's computable and what's not; what's left to say? Of course lots of things are left to say, but the article doesn't really talk about them. --Trovatore 22:28, 8 February 2006 (UTC)

text: Ah, that's not bad. Then there'd be room to do the sort of thing I outlined, with lots of sections that point to main articles and give brief summaries of their contents. There could be one of those sections for automata theory, too. Note that I'm not personally promising to take care of the second part of the plan, at least not soon (any large time block that I commit to WP at the moment would have to be at set theory, naive set theory, axiomatic set theory, where I've won a mild consensus for an ambitious reform). --Trovatore 23:00, 8 February 2006 (UTC)
thread_title: structure of article, recursion theory

message: What about Universal Turing Machines? Shouldn't they be included as well? 70.111.251.203 14:42, 7 March 2006 (UTC)
thread_title:  Universal Turing Machines 

message: Found use of first person.  While text is clear and easy to understand, it is still bad style. 210.50.201.22 05:35, 26 May 2006 (UTC)
thread_title:  Cleanup 

message: How is the following statement confusing? "Actually, these are computer programs written in general-purpose programming languages which are Turing Machines (the GP languages are, therefore, called Turing-complete), while the actual computers executing the programs are FSMs." I have included it into the article even before looking into the discussion to disambiguate the popular confusion: "Poll: Are PCs Turing Machines?" Thi is the actual and vast confusion. What I see at this page proves my doubts. Please explain what is so confusing in my sentence? Peahaps it is rather wrong or inappropriate? --Javalenok 09:02, 13 June 2006 (UTC)
replies: text: I don't know what "confusion" you're referring to. Your statement is accurate, but the English is difficult to understand, and I'm not sure how much it adds in this context. Dcoetzee 22:30, 30 January 2008 (UTC)
thread_title:  confusion PCs are not FSMs 

message: This discussion is copied from the user page.
You changed Church-Turing thesis to claim that it had been disproven.  This is certainly not the case. Please feel free to discuss your changes on the talk page of the article. CMummert · talk 10:49, 12 April 2007 (UTC)
replies: text: The Church-Turing thesis has not been disproved.  However, it needs to be stately precisely which was not done in the previous version of the article.  It is very important to distinguish between computable functions and computability (computations).--71.198.216.63 16:11, 12 April 2007 (UTC)
thread_title:  Church-Turing thesis 

message: I don't understand this idea. What does it mean to decide a language? Unfree (talk) 16:32, 30 January 2008 (UTC)
replies: text: To decide whether a given string is in the language or not. --Trovatore (talk) 20:11, 30 January 2008 (UTC)
thread_title: Deciding a language

message: For anyone keeping this article on their watchlist: there is currently an attempt at merging a number of articles on (non-)recursive/(un)decidable/(un)computable sets/languages/decision problems into a single, thorough article. The experiment currently sits at Recursive languages and sets. Comments are very welcome. Pichpich (talk) 00:43, 21 February 2008 (UTC)
thread_title:  Attempt to merge 

message: This is a duplicate post from Talk:Algorithm#A_paradoxical_situation. To keep the discussion in one place, please comment there is you are interested. — Carl (CBM · talk) 20:43, 19 March 2008 (UTC)
thread_title:  A paradoxical situation 

message: There is a discussion currently at Talk:Recursion theory#Reorganize the Computability articles about reorganising the computability articles to get some sort of hierarchy. In particular the thinking is that Computability should be an introduction rather than a disambiguation page. Dmcq (talk) 11:26, 14 August 2009 (UTC)
replies: text: The reorganization is underway. The centralized discussion is at Talk:Recursion theory#Reorganize the Computability articles. — Carl (CBM · talk) 14:52, 22 August 2009 (UTC)
thread_title:  Reorganize the Computability articles