Talk:Decision problem

message: I did a complete rewrite of the article. The main problems I tried to fix were
#article to verbose without using any well defined concepts
#mixed word problem (computability) with general concept of decision problem, which I think should be separate
MathMartin 13:46, 19 Nov 2004 (UTC)
replies: text: I like the brevity, but it seems to focus strongly on computability theory, particularly in the examples section. I'll add some example problems important in complexity theory and make a note that the list is only a few important examples. Deco 18:55, 19 Nov 2004 (UTC)
thread_title: Complete rewrite

message: I thought Wikipedia is an encyclopedia, not an entry-portal to an article in the AMS. I's a pretty tough read for a non-specialist. A budding mathematician (e.g. interested undergrad or high-school math whiz or engineer/scientist not in the field) would be stumped. One place to start would be some relatively examples or a progression from an "easier read" into the deep stuff (or visa versa, but both). Ideas? wvbaileyWvbailey 17:14, 10 January 2006 (UTC)
thread_title:  Examples, Simpler Please 

message: I am moving this from the main page for now.
:It should be noted that a decision problem is always a set of related problems which is in some sense large enough. A single problem P is always trivially decidable by assigning the constant function f(P)≡0 or f(P)≡1 to it.
:Nearly every problem can be cast as a decision problem by using reductions, often with little effect on the amount of time or space needed to solve the problem. Many traditional hard problems have been cast as decision problems because this makes them easier to study and to solve, and proving that these problems are hard suffices to show that more complex problems are hard as well.
The first paragraph makes no sense to me.  The second seems to have a definition of problem different than decision problem, although the article gives no such definition. 
I added a section explaining the equivalence of decision problems and function problems, which I think does an adequate job of replacing the above paragraphs. CMummert 00:11, 27 August 2006 (UTC)
thread_title:  Notes section 

message: The article on Recursive set states that any language which is not decidable/computable is undecidable.  Here, a language that is not decidable may be either semidecidable or undecidable.  Are these separate categories or the same?  That is, is a recursively enumerable set considered to be a kind of uncomputable set? 67.180.32.231 08:08, 1 April 2007 (UTC)
replies: text: Yes, a recursively enumerable set that is not recursive is both semidecidable and undecidable. CMummert · talk 12:24, 1 April 2007 (UTC)
thread_title: Definition Conflict

message: Would someone be so kind as to refer me to the source for this result mentioned in the article?  "However, this reduction is more liberal than the standard reduction used in computational complexity..." and so on, about the complexity of characteristic functions differing from standard complexity.  I don't see it in Sipser, and I'd like to learn more. 128.32.192.124 01:04, 20 April 2007 (UTC)
replies: text: The user who made that edit gave the following reference  and said to look at the appendix. I think that the article is just trying to point out that computational complexity tends to use many-one reductions rather than Turing reductions, but it could be worded more clearly. CMummert · talk 01:14, 20 April 2007 (UTC)
replies: text: Thank you so much!  I agree that it should probably simply be rewritten to state what you're saying, although for now I will add the reference. 67.180.4.242 22:15, 21 April 2007 (UTC)
thread_title: Reference

message: Is it possible to give a simple example of a decision problem that is not decidable?  I checked the referenced article that lists undecidable problems, but they all require too much brainpower to grasp to be useful as an example of the concept.  I'm wondering if maybe there are trivial undecidable problems that aren't interesting, but at least demonstrate the concept.  Bryan Henderson 15:45, 21 June 2007 (UTC)
replies: text: A popular one for just this purpose are tiling problems, such as those described by Wang tiles. Reference here. Dcoetzee 01:23, 22 June 2007 (UTC)
thread_title: Undecidable problem example?

message: :However, this reduction is more liberal than the standard reduction used in computational complexity (sometimes called polynomial-time many-one reduction); for example, the complexity of the characteristic functions of an NP-complete problem and its co-NP-complete complement is exactly the same even though the underlying decision problems may not be considered equivalent in some typical models of computation.
Maybe expand or at least point to some references?  — Preceding unsigned comment added by 97.81.29.81 (talk) 01:03, 10 July 2012 (UTC)
thread_title:  too weasly for wiki? 

message: I've changed the importance of this page from "low" to "mid". Actually, I think it rates a "high", but philosophers who are not mathematicians may think differently. The subject of the page is the impossibility of deciding every question that can be posed. Rick Norwood 19:39, 7 September 2007 (UTC)
replies: text: I'm neither mathematican nor a philospher and I think it could be mid-to-high, at least from a (mathematics) foundational and historical perspective. In particular it has application to the philosophy of mind (that's the secret reason for my interest). Some writers fault the philosphers for not understanding the issues at gut-deep level but nevertheless concocting dubious pronouncements and arguments (e.g. not understanding quantum mechanics re philosophy of mind; also all the examples in Torkel Franzen 2005 Godel's Theorem: An Incomplete Guide to this Use and Abuse, A K Peters, Ltd. Wellesley MA). Another reason is: all three proofs of the 1930's that were so significant -- Church 1936, Turing 1936-7, Kleene 1943 -- all revolve the unsolvable "decision problem", and they all use similar techniques to arrive at their proofs (conversion of proofs to numbers, their subsequent enumeration (listing) and Cantor's diagonal argument). Godel 1931 (his theorem VI, the so-called first incompleteness theorem) is also a proof of undecidability and follows a similar tack. Is any of this of use to philosphers constructing arguments? I dunno, but I would hope so. wvbaileyWvbailey 21:52, 7 September 2007 (UTC)
thread_title: Importance

message: I am very disappointed that there is no mention, either in the article or this talk page, of Alfred Tarski's theorems (in 1936) that truth is undefinable (see Indefinability_theory_of_truth). Hccrle (talk) 01:24, 1 October 2009 (UTC)
replies: text: After reading this I consulted Grattan-Guiness (2000) The Search for Mathematical Roots 1970-1940 pp. 551-553. I see some interesting stuff, but nothing about his contributions to the Engscheidungsproblem, nor about "truth is undefinable". In fact, Tarski's truth is definable by going outside the formal system (theory) into the metasystem (metatheory); Grattan-Lewis in fact gives Tarski credit for the names "metalanguage" and "metatheory). To make the point, Grattan-Guiness gives the example directly from Tarski: '"it is snowing" is a true sentence if and only if it is snowing'" (Tarski 1936a, 156)(cf Grattain-Guinness 200:552). Bill Wvbailey (talk) 18:42, 1 October 2009 (UTC)
thread_title: Lack of mention of Tarski's theorems

message: What has the reference to Whitehead and Russell at the end of the article got to do with the subject matter? 213.122.67.212 (talk) 12:52, 6 November 2010 (UTC)
replies: text: The "vicious circle" paradoxes and the Entsheidungsproblem derive from the same problem of self-referencing propositions, i.e. impredicativity. The article is pretty thin and doesn't get into this. BillWvbailey (talk) 13:46, 6 November 2010 (UTC)
replies: text:  The negative solutions (Church's and Turing's) of the Entsheidungsproblem were found by a kind of self-reference (though that's not a phrase I'd use), but Hilbert's Entsheidungsproblem didn't (I shall boldly claim) derive from "self-reference". 213.122.62.19 (talk) 17:35, 11 November 2010 (UTC)
thread_title: Reference to Whitehead and Russell

message: This section states: "Turing reduced the halting problem for Turing machines to the Entscheidungsproblem."
: I don't think this is accurate. Turing & Church showed that deciding provability of arithmetic statements could be used to decide the Halting Problem, which really means that the Entscheidungsproblem was reduced to the halting problem and not the other way around? — Preceding unsigned comment added by Froskoy (talk • contribs) 08:28, 5 February 2013 (UTC)
thread_title: Negative solution[

message: I have fixed the incorrect date on Turing's 1936 paper. The footnote at the end of Bob Soare's 1996 paper "Computability and Recursion": [www.people.cs.uchicago.edu/~soare/History/compute.pdf] has a good explanation of the correct dates. The reprint of Turing's paper in the collection edited by Martin Davis, (which was referenced before) only says that the reprint is from ser. 2, vol. 42 (1936-7), pp. 230-265, so I don't think the previous explanation of the date is justified from that book. As far as I can tell, the dating is incorrect in MathSciNet, (explaning many people incorrectly referencing the paper from 1937), but it is correct in Zentralblatt. — Preceding unsigned comment added by 131.215.108.224 (talk) 21:32, 1 May 2013 (UTC)
thread_title: Date of Turing's paper

message: I changed the hatnote to "otheruses4" to be more clear about what kind of output is intended. The "about" template can make many kinds of output, but this article is intended to use the one produced by "otheruses4".  I also changed the ISBN magic links syntax to use the new ISBN template, because ISBN magic links will be disable sometime soon. I think it is clearer to use "template:" in these. — Carl (CBM · talk) 23:19, 15 April 2017 (UTC)
replies: text: Ok, but what is the reason for including all those "template:" namespace things in your templates? The whole point of putting things into template space is that you can then use them as templates without having to specify the namespace. —David Eppstein (talk) 00:09, 16 April 2017 (UTC)
replies: text: You can use them either way - both methods are completely equivalent from the point of view of the software. For the ISBN templates in particular, I think it is helpful to emphasize that the template version is being used instead of the magic link. I am starting to think that the longer version may be more clear in general. I have been working my way through the computability theory category looking for cleanup and expansion opportunities, and converting the ISBN magic links as I go. — Carl (CBM · talk) 00:14, 16 April 2017 (UTC)
thread_title:  Cleanup 

message: According to the Encyclopedia Br.:
 
"decision problem, for a class of questions in mathematics and formal logic, the problem of finding, after choosing any question of the class, an algorithm or repetitive procedure that will yield a definite answer, “yes” or “no,” to that question. The method consists of performing successively a finite number of steps determined by preassigned rules. In particular, the term is used for such procedures for finding whether—in a particular logistic system, logical calculus, or formal mathematical system—some given “well-formed formula” (generated in accordance with established formation rules) is or is not provable as a theorem of the system."
not the question is the decision problem, but the search for an algoritm. Madyno (talk) 22:13, 18 August 2022 (UTC)
replies: text: If you have a question, or a suggestion for improvement of the article, your writing makes it unclear. In any case, a problem and a method for solving the problem are two different things. —David Eppstein (talk) 22:42, 18 August 2022 (UTC)
replies: text: As I'm not familiar with decision problems, I hope to hear comments on what I found. Furthermore it would be clearer if it is explained why the set of inputs need to be infinite. Madyno (talk) 09:57, 23 August 2022 (UTC)
thread_title:  Definition 

message: The picture included in the article is misleading at best. If the decision problem is undecidable then no such algorithm exists, however the universe of discourse is still partitioned by question. For example, every Turing machine either halts or it does not, this gives a partition of the set of all Turing machines into halting and non-halting, even if there is no general way of deciding if a machine belongs in the halting set.  — Preceding unsigned comment added by Gillchild (talk • contribs) 06:41, 7 February 2024 (UTC)
thread_title:  Decision problem picture misleading