# Notes

1. Provide various equivalent notions of computability ranging from Turing computability to Abacus computability to general recursive computability.
2. Outline computability of total, partial, and uncomputable functions, giving examples for each.
3. Parse and conjoin function problem with and revert to, what I take to be the more correct, computation problem - viz., this article (unless someone objects?). Nortexoid 04:58, 23 Nov 2004 (UTC)

I think (1) should be discussed on computability theory. (2) is already partially discussed on computable function. Regarding (3), I do not know if computation problem is widely used in this sense. I have only heard and read the terms decision problem and function problem. The complexity classes for function problems are also prefixed with an F (like FP) so I think it makes more sense to stick with this term. MathMartin 18:51, 28 Nov 2004 (UTC)

In mathematical logic, 'computation problem' is more often used than 'function problem'. See G. Boolos' widely used "Computability and Logic" and Kleene's "Mathematical logic" and "Introduction to Metamathematics" for starters. It might be used more often in mathematics (non-logic), but I haven't a clue.
I cannot quote any books on this topic and google did not provide an answer, so perhaps we should use your term. In any case I do not really care, but perhaps other people have a stronger opinion.MathMartin 13:28, 29 Nov 2004 (UTC)
As for (1) - ok; and the overlap for (2) is still necessary, if you ask me. It makes the article more informative and self-contained without linking/referrign all over the place. Nortexoid 00:15, 29 Nov 2004 (UTC)
I think it is ok to duplicate some material in order to provide context for an article. But in the long run we want to have a set of core definition (articles) which are referenced from other articles. And in my opinion the computability and computational complexity articles lack those core articles and duplicate a lot of material, which makes it hard to keep the articles consistent. But anyway if you are interested in writing the computation problem article give it a try. MathMartin 13:28, 29 Nov 2004 (UTC)
I'm not suggesting that we provide in-depth analysis of the above topics. I.e., mention in one sentence that there are equivalent ways of solving a computation problem - i.e., by abacus machines, Turing machines, general recursion, etc. For #2, mention that computable function are recursive (partial or total), and that Turing machines will always halt for any input when computing total functions, but not partial ones. And perhaps instead of redirecting function problem, a link in "See also" can be added. Anyway, if nobody adds to the article before I have time to do it myself, then I'll go ahead and do it. Nortexoid 06:49, 1 Dec 2004 (UTC)

## First sentence of article

I'm very confused by the first sentence of this article. A computation problem is "determining whether or not there exists a computation procedure"? So the computation problem is "given a class S of questions, determine whether an algorithm exists to solve this class"? And then you'd have to design a Turing machine that figures out whether algorithms exist to solve certain classes of questions? That sounds like the wrong level of abstraction. Is a computation problem actually the same as a function problem? I guess I just don't understand how "determining whether an algorithm exists" has to do with the definition of a problem as a mathematical entity. -- Creidieki 20:58, 1 April 2006 (UTC)

## rewrite: computation vs. computational vs. function

I think the previous revision was trying to say that a computation problem was a problem where something is "computed", i.e., a function problem. The current rewrite seems to be saying that a computation problem is the same as a computational problem, i.e., including both function and decision problems. I'm not very clear on the naming here, frankly. -- Creidieki 12:39, 20 November 2006 (UTC)

Oh I wasn't aware that the latter existed. Then this page should be a redirect. I don't think I've ever seen the term "computation problem" used in the context that the earlier version suggested. Moreover, there is no article linking to it. So I'll just redirect to computational problem. Pascal.Tesson 14:11, 20 November 2006 (UTC)