Talk:Complexity class

message: I'm surprised there aren't pages for linear time, log(n) time, or even constant time.  They're not as intriguing as P vs. NP, but many important (albeit ordinary) tasks require knowing about the distinctions between these complexity classes, eg. when to use linked lists vs. arrays or vectors.
Any thoughts?
:These are only really useful in the analysis of algorithms with regard to particular machine models; for example, most sorting algorithms assume that you have random access, that the input has a particular structure, and that a comparison or exchange is a unit operation. In complexity theory, we try to avoid any such assumptions by using classes that are invariant over a large class of abstract machines, like P, NP, and L.
:For example, anything you can do on a random access machine in polynomial time, you can also do on a Turing machine (with or without multiple tapes) in polynomial time. If the input is a graph, you can specify it in adjacency matrix form, adjacency list form, or incidence matrix form - in these coarse classes, it doesn't matter. You can't say that about the classes you mention. In fact, a Turing machine can't do much of anything useful in log time, although a random access machine can.
:This might be (should be?) discussed somewhere in the encyclopedia. Deco 22:36, 28 Apr 2005 (UTC)
thread_title: Sublinear time classes

message: In the Table it seems that BQP\subseteqNP. However in the BQP article it is stated that BPP\subseteqBQP. In the BPP (complexity) article it is stated that it is an open question whether NP contains BPP. So who is wrong? Chithanh 14:55, 30 March 2006 (UTC)
replies: text: It shoud be that BPP \subseteqBQP. No other inclusions are known between the classes BPP,BQP and NP.  —Preceding unsigned comment added by 130.235.35.227 (talk) 08:38, 18 October 2007 (UTC)
thread_title:  Relationship between BPP, BQP and NP 

message: Reading P, NP, P-complete, etc, I see that there's a lot of variation in how easy the articles are to read for someone with little math knowledge.  Would it be possible for all articles to have a very gentle paragraph to introduce simplistic examples, or perhaps for a single very-gentle introduction covering complexity classes to be created?  For this target audience (ie, people like me) it's often a good idea to show why problems are (or aren't) hard.  Thus, for factorisation it's useful to give an example of two big prime numbers, (and maybe mention where numbers this big are used, perhaps in some common web crypto?) and their product, and then say that "If you can do x calculations per second it'll take you y seconds to solve this problem".  The subset sum problem is used as an example, yet the subset sum problem page doesn't have clear, easy, beginner's level examples to explain it.  Dan Beale 13:23, 31 July 2007 (UTC)
thread_title:  Variability of ease-of-reading across complexity class articles 

message: Hey, so according to your chart NP is a subset of P. But over here P=NP it looks as though the opposite is true. What gives?Solsticefan (talk) 04:58, 28 April 2009 (UTC)
replies: text: Huh? I think you're reading the chart backwards. Ben Standeven (talk) 05:50, 24 December 2009 (UTC)
thread_title: Here's one for you

message: The following statement is in error: "being able to reduce another problem, Π1, to a known NP-complete problem, Π2, would indicate that there is no known polynomial-time solution for Π1".  Reducing a problem Π1 to an NP-complete problem only tells you that Π1 is at worst NP. It says nothing about how easy Π1 is.  I'm not sure what the author originally had in mind:  perhaps "being able to reduce a known NP-complete problem, Π2, to another problem, Π1, would indicate that there is no known polynomial-time solution for Π1"?
Ross Fraser (talk) 23:33, 12 April 2010 (UTC)
thread_title:  Error in Reduction section 

message: Are they correctly written in BOLDFACE? Or in normal ROMAN uppercase? I can guess myself only that they may not be written AS HERE. Incnis Mrsi (talk) 15:20, 27 May 2013 (UTC)
thread_title:  Names of classes