Talk:Computational complexity theory

message: I wonder where would be a good place to mention that we know some problems not in P, for instance Presburger arithmetic. --AxelBoldt
I've added it to Complexity classes P and NP.  It should also be added to EXPTIME, whenever someone gets around to writing it.  I would put it under P too, except that's more of a redirect than a real article.  --LC
----
I've added a note explaining (in brief) what the Co classes are.  What do you think about trying to consolidate many of these articles?  For example, NP and Co-NP should probably be the same article, as should NP-complete and Co-NP-complete
GulDan 18:10, 31 Jul 2003 (UTC)
thread_title: older entries

message: This article was removed from being a featured article with the following comments that may be helpful in improving the article: 
How on Earth did this get featured? No mention of models of computation. No mention of Turing machines! No explanation of non-determinism. Nothing about randomized algorithms. Nothing about parallel computation and the structure of P. Nothing about reduction. No pictures. No history. Gdr 08:40, 2004 Jul 26 (UTC)
*Support removal.  The weird thing is that I don't even see this article on Wikipedia:Featured article candidates/Featured log.  When the WP:FA page was new, a lot of people added articles themselves, as the candidate process was kind of unclear. - DropDeadGorgias (talk) 17:02, Jul 26, 2004 (UTC)
* Support removal; this is nowhere near comprehensive. — Matt 17:32, 27 Jul 2004 (UTC)
thread_title: Featured article removal

message: Work is currently in progress on a page entitled Views of Creationists and mainstream scientists compared.  Also currently being worked upon is Wikipedia: NPOV (Comparison of views in science) giving guidelines for this type of page.  It is meant to be a set of guidelines for NPOV in this setting.  People knowledgable in many areas of science and the philosophy of science are greatly needed here.  And all are needed to ensure the guidelines correctly represent NPOV in this setting.  :)  Barnaby dawson 21:12, 29 Dec 2004 (UTC)
replies: text: We don't need a plethora of articles detailing everybody's views on this highly controversial topic.  Wikipedia is an encyclopedia, not a platform for expressing various distorted politico-quasi-religious pseudoscientific views.  For further information on creationism, the reader is referred to the Bible.  There is an article on so-called intelligent design, which already pushes the limits of what is acceptable on Wikipedia, although the "concept" does seem to be widely reported in the mass media.  And what on earth has this got to do with computational complexity theory? -- 130.94.162.61 15:17, 24 December 2005 (UTC)
replies: text: This is clearly moot now.  Barnaby dawson 17:52, 24 December 2005 (UTC)
thread_title: "Invitation" to work on questionable off-topic article

message: The Good article nomination for  has failed    
:I think the reasons that led the article from losing FA status (which it probably should never have had in the first place) are still reasons not to give the article GA status. I know most people don't read german but if you look at the german page you can still see a much more elaborate structure, pictures and so on. The current article fails the GA criteria in a number of ways: slightly narrow focus, certainly less than "compelling prose", not enough references and so on. As someone who works in the field, there are also a number of things in the article that make me cringe like "The most important complete set is NP-complete." Well, so fix it I guess... but in the meantime it's way too early to give the article GA status.
 Pascal.Tesson 03:34, 11 July 2006 (UTC)
thread_title:  [[Wikipedia:Good articles|Good Article]] [[Wikipedia:Good articles/Nominations|nomination]] has failed 

message: I am working on re-writing at least parts of this article.  I understand computational complexity theory well, though I am by far not an expert on it, so my knowledge of some specific areas are lacking.  Feel free to help out, intervene or to give suggestions.--Konst.able 09:00, 9 October 2006 (UTC)
thread_title:  Fixing this up 

message: I noticed this article in the "pages needing attention" section of the Computer Science project page.  I understand that it's already undergone one major rewrite (which I will look over in detail when I have some time) but I have some thoughts off the top of my head that I'd like to share:
# Shouldn't this article be called "Run-time complexity theory"?
# In the opening graf, "scalability" is used to describe algorithm complexity.  While this is perhaps an apt analogy, isn't it technically inaccurate to equate the two concepts?  "The capacity to handle increasing workloads/throughput" isn't quite the same thing as "the increase in running time as input size increases".
# The Big-O function is mentioned in passing.  Small-O, Omega and Theta are not mentioned at all.  Neither are the concepts of monotonically increasing functions or asymptotic limits.  Shouldn't these concepts be central to the article?
# I didn't notice any discussion of why theoretical run-time complexity classes are superior to empirical measurements or benchmarks.  When I learned run-time complexity, a "classic" example we were given right off the bat was a side-by-side comparison of running times for two machines running two different sorting algorithms.  Machine A was the equivalent of a 1980's TRS-80, running an O(n lg n) sort.  Machine B was a state-of-the-art (at the time) Pentium 4 running an O(n3) sort.  For small sizes of n, Machine B was light-years faster, but as the size of n increased, Machine A eventually came to pwn Machine B.  I'd like to see a chart like that in the article.
I'll give the page a thorough read and make more detailed suggestions later. Groupthink 13:16, 26 June 2007 (UTC)
replies: text: I've added a run-time analysis article. Groupthink 21:02, 28 June 2007 (UTC)

text: I disagree. There is already a P/NP page elsewhere. And the majority of complexity theory deals with run-time complexity. P/NP is only included here because of its fundamental importance in complexity theory and computer science in general. If anything, the P/NP could be toned down, and the reader directed to the other page. But thanks for working on this. It could really help from your input. Scottcraig 17:13, 30 June 2007 (UTC)
replies: text: Then perhaps computational complexity theory should be merged into run-time analysis, and the material on boolean decidability and P/NP-completeness in comp. complexity should be merged into Boolean satisfiability problem and Complexity classes P and NP respectively? Groupthink 21:42, 30 June 2007 (UTC)
thread_title:  Fixing this up again 

message: On second thought, run-time complexity really deserves its own article, and the thrust of this article should remain P- and NP-completeness. Thoughts? Groupthink 02:04, 27 June 2007 (UTC)
replies: text: I've added a run-time analysis article. Groupthink 21:02, 28 June 2007 (UTC)

text: I disagree. There is already a P/NP page elsewhere. And the majority of complexity theory deals with run-time complexity. P/NP is only included here because of its fundamental importance in complexity theory and computer science in general. If anything, the P/NP could be toned down, and the reader directed to the other page. But thanks for working on this. It could really help from your input. Scottcraig 17:13, 30 June 2007 (UTC)
replies: text: Then perhaps computational complexity theory should be merged into run-time analysis, and the material on boolean decidability and P/NP-completeness in comp. complexity should be merged into Boolean satisfiability problem and Complexity classes P and NP respectively? Groupthink 21:42, 30 June 2007 (UTC)
thread_title:  Run-time complexity 

message: Currently, asymptotic complexity redirects here. This seems wrong to me - it ought to redirect to a page more like big O notation that actually explains the concept of asymptotic complexity in a much more specific setting. But I'm not sure just where to point it to. What do you think? Dcoetzee 03:53, 7 July 2007 (UTC)
replies: text: Either asymptotic analysis or run-time analysis? Groupthink 04:25, 7 July 2007 (UTC)
thread_title:  Asymptotic complexity 

message: This section of the article has been rubbing me the wrong way since the first time I saw this article. I don't see it's relevance, I don't believe that it fits in with Wikipedia's WP:LIST guideline, and the criteria for inclusion of a researcher in that list is uncertain (for one: why is Turing not on the list?)  Perhaps it is time to split it out into a new article (List of researches in computational complexity theory) or remove it altogether, leaving only the most vital people relevant to the field (such as Cook, Turing and Knuth) in the See also section.--Konstable 11:05, 7 July 2007 (UTC)
thread_title:  Notable Researchers 

message: This page could use some history - in particular it ought to reference Juris Hartmanis and Richard Stearns' "On the Computational Complexity of Algorithms". It already cites a reference with some history. I can help with this. Dcoetzee 03:02, 18 August 2007 (UTC)
thread_title:  History 

message: What kind of machine is used to measure the number of steps or amount of memory required to solve a problem?  A RASP machine?  I don't think it's a Turing machine.  --Doradus (talk) 05:42, 18 December 2007 (UTC)
replies: text: The definitions of major classes are explicitly designed to be robust against "reasonable" changes in the definition of the underlying abstract machine. In typical presentations various types of Turing machines are used but it doesn't matter - RAM models, cache-oblivious models, pretty much everything works fine. That's why we discuss P and not, say, DTIME(n3). Dcoetzee 20:20, 18 December 2007 (UTC)
thread_title:  What machine model? 

message: Bit complexity redirects to this article, but unfortunately the article does not explain what this means. What is it? Thank you. --Abdull (talk) 19:48, 24 July 2008 (UTC)
replies: text: Bit complexity refers to a measure of time complexity where the only operations assumed to operate in constant time are operations that act on single bits. I personally think it should be discussed in another article that compares and contrasts it with models where log-sized words are the unit. I'm not sure what such an article would be called. Dcoetzee 21:27, 24 July 2008 (UTC)
replies: text: Thank you for your answer. I'd be great if there was an article about the topic you mentioned (because, for example, I cannot imagine what a log-sized word unit is yet). In the meantime, I stumbled upon another redirect, asymptotic complexity which defies definition. --Abdull (talk) 09:02, 25 July 2008 (UTC)
replies: text: Good idea. For lack of a better name, I've created a new article called Context of computational complexity describing many factors that affect complexity analyses, including the bit/word complexity distinction. Dcoetzee 21:42, 26 July 2008 (UTC)
replies: text: Thank you very much! Now, only asymptotic complexity has to be explained (please! :). --Abdull (talk) 14:47, 30 July 2008 (UTC)
replies: text: That's just a bad redirect. :-) Asymptotic complexity is nothing but complexity metrics described using asymptotic notation. For now I redirected it to Big O notation. Dcoetzee 17:32, 31 July 2008 (UTC)
replies: text:  Asymptotic complexity now redirects here again. This article is good, but it doesn't contain the word "asymptotic" at all. The Big O notation might be a better redirect. Werediver (talk) 14:44, 9 June 2021 (UTC)
replies: text:  Now,  is a redirect to Computational complexity#Asymptotic complexity. D.Lazard (talk) 14:58, 9 June 2021 (UTC)

text:  As Context of computational complexity is a content fork of Computational complexity, and is a unplausible research term, I have redirected it to Computational complexity. Also, I have redirected  to the same article, which I have edited for adding details to the definition of bit complexity. D.Lazard (talk) 18:11, 9 June 2021 (UTC)
thread_title:  Bit complexity and asymptotic complexity

message: The article does a poor job in failing to point out it is heavily biased towards worst-case analysis/worst-case complexity (and there are no articles explaining this concept). I threw in a phrase into the overview section, but someone has to make a prominent point on the issue in the article, since this is a fundamental concept. Probably a whole section about worst/case/average caes, upper/lower bounds, etc. Unfortunately I am not a man for the job. Twri (talk) 19:21, 24 February 2009 (UTC)
thread_title:  worst-case analysis 

message: I think this is better now but is nowhere near perfect; I hope at least it gives something for others to get hold of.
I think there are two main problems:
*NP problem is covered too much, it has its own article. I have tidied it up with the view that much of it may be merged with that article.
*Laziness by previous editors in adding references but not properly. Takes me forever, I have done some but there are plenty left where the article proper gives a link but not as a ref.
Hope on the whole it is an improvement.
SimonTrew (talk) 03:46, 17 March 2009 (UTC)
thread_title:  OK done big edit 

message: "The fact that the P − NP problem has not been solved, and indeed has been shown to be unsolvable..."  Is this right, and if so, reference?  —Preceding unsigned comment added by J. Holden Caulfield (talk • contribs) 17:34, 31 March 2009 (UTC)
replies: text: This is not what Gödel's Incompleteness Theorem is about. It just says that for a "sufficiently strong" logic+theory, there are statements that must be labeled "true" but cannot be proved within that system (but possibly can be proved via another meta-system) (Also, Gödels canonical example of a self-referential statement has a bad smell as frankly it seems to me he intermixes truth values from different levels with scant justification, but that's another topic). If you stay in First-Order Logic + Some Theory (e.g. Arithmetic), it intuitively seems correct to say that if "problems that are easy to check are easy to solve" (i.e. P=NP) then "finding a proof" of a provable statement should be about as easy as "checking a proof" of a provable statement (which is known easy). This needs to be made more precise of course. There is a T101 in your kitchen (talk) 21:22, 8 October 2016 (UTC)
thread_title:  P-NP not solvable? 

message: The section on graph theory is little more than a link to the graph theory page. The text inside doesn;t really referenc graph theory that much, or at least it doesn't explain the connection in graph theoretic terms. Perhaps it could be expanded, or removed? Any thoughts? 86.145.23.98 (talk) 13:57, 9 May 2009 (UTC)
replies: text: I agree. Actually, the whole article is in bad shape. It probably has to be re-written entirely to give it a coherent structure... Pichpich (talk) 17:44, 23 May 2009 (UTC)
thread_title:  Graph Theory 

message: Kolmogorov Complexity (length of generating program for given data), rather than run time, is what many if not most people would mean by 'Computational Complexity', and this article should refer to it early on with a reference to its Wikipedia article. Other than that, I'm not sure that the material covered in the article is actually a 'subject' per se. P = NP is a legitimate subject: so are algorithmic design, cryptography, etc. The mere design of a notation about how long something takes to run, isn't much of a subject. The little o and big O notations, for instance, have many other uses in math unrelated to algorithm runnning time: I hope they have a separate article.  —Preceding unsigned comment added by 63.229.11.118 (talk) 04:55, 18 June 2009 (UTC)
replies: text: I strongly disagree. As I said a few lines above: Compare the recent books by Arora and Safra: "Computational Complexity: A Modern Approach" (draft available online) and by Goldreich: "Computational Complexity: A conceptual perspective" (drafts of some chapters available online). It IS indeed a subject on its own, and is as such different from Kolmogorov complexity. Hermel (talk) 18:19, 21 June 2009 (UTC)

text: Yes, I also disagree that "many or most people" would think computational complexity is Kolmogorov complexity.  --Doradus (talk) 20:00, 14 October 2009 (UTC)
thread_title:  Needs some kind of note/cross-reference to Kolmogorov Complexity, and other remarks 

message: I removed this text from the article:
The field was subsequently expanded by many researchers, including:
 
<-- 
This is NOT a "Hall of Fame". All people with wikipedia articles are notable.
Please add only names which are described as "groundlayers" by the peers,
with citations and summary of major contributions 
-->
* Manuel Blum
* Allan Borodin
* Stephen Cook
* Michael Fellows
* Michael R. Garey
* Oded Goldreich
* Juris Hartmanis
* David S. Johnson
* Richard Karp
* Marek Karpinski
* Donald Knuth
* Leonid Levin
* Christos H. Papadimitriou
* Alexander Razborov
* Richard Stearns
* Leslie Valiant
* Andrew Yao
We need to establish some criteria for inclusion, or not have such a list at all. I haven't seen such lists on other articles either. The article on physics doesn't have a list of notable physicists like Newton, Einstein, etc. --Robin (talk) 18:26, 14 October 2009 (UTC)
thread_title:  List of complexity theorists 

message: This image shows the relationship between computability theory, complexity theory and formal language theory. I had originally put it in the lead section, but it takes too much space and makes the lead look bad. Any suggestions on where this might go (including new sections which haven't been written yet)? --Robin (talk) 13:13, 26 October 2009 (UTC)
replies: text: Could we perhaps have a hyperlinked version of the image in the "See also" section (so that we would have an illustrated "see also" section instead of the usual boring list of links)? Or perhaps we could replace the navigation box  with this (at the very bottom of the page)? — Miym (talk) 00:12, 4 November 2009 (UTC)
replies: text:  I would prefer putting it in the "see also" section. Another idea I had was to put this in the history section, with a subsection devoted to how complexity theory is historically related to computability theory and formal language theory. --Robin (talk) 01:13, 4 November 2009 (UTC)
thread_title:  Image relating complexity theory and other fields 

message: Someone watching this article might have noticed that I've been editing it for the last few weeks trying to improve it. I'd really like to hear suggestions / comments / criticisms to improve it further. Of course, you can be WP:BOLD and improve the article yourself, but if you don't have the time or inclination to do so, I would appreciate any comments you have to improve the article. Any topics you feel that must be mentioned in the article and haven't been covered adequately? Any topics covered too much in detail? --Robin (talk) 22:45, 3 November 2009 (UTC)
replies: text: One of my concerns is the illustration in Computational complexity theory#Theory vs. practice. There seems to be some serious confusion regarding how to read the plot and what it means. Could we simply remove it, as well as all discussion that refers to it? — Miym (talk) 23:42, 3 November 2009 (UTC)
replies: text: Yes, sure. I'm not a fan of that myself. The whole section on intractability is a bit sketchy, but I'm not too sure how to present it properly. It feels like a "criticisms of complexity theory" section, but presented badly. There might be interesting things to mention in such a section, like the fact that SAT solvers in reality to do handle largish instances (10000+ variables) in practice, and that even though problems might be hard to solve exactly, they might be easy to approximate. I'll see if I can get more information on this and write some stuff up. --Robin (talk) 23:56, 3 November 2009 (UTC)
thread_title:  Improving this article 

message: Which one of the following seems better for presenting information?
Complexity class	Type of problem 	Model of computation            	Bounded resource	Bound for the resource
DTIME(f(n))     	Decision problem	Deterministic Turing machine    	Time            	f(n)
P               	Decision problem	Deterministic Turing machine    	Time            	polynomial
EXPTIME         	Decision problem	Deterministic Turing machine    	Time            	exponential
NTIME(f(n))     	Decision problem	Non-deterministic Turing machine	Time            	f(n)
NP              	Decision problem	Non-deterministic Turing machine	Time            	polynomial
NEXPTIME        	Decision problem	Non-deterministic Turing machine	Time            	exponential
OR a list, like this:
 
* DTIME(f(n)): Decision problems solvable by a deterministic Turing machine within time f(n).
* P: Decision problems solvable by a deterministic Turing machine within time polynomial in the input size.
* EXPTIME: Decision problems solvable by a deterministic Turing machine within time exponential in the input size.
* NTIME(f(n)): Decision problems solvable by a nondeterministic Turing machine within time f(n).
* NP: Decision problems solvable by a nondeterministic Turing machine within time polynomial in the input size.
* NEXPTIME: Decision problems solvable by a nondeterministic Turing machine within time exponential in the input size.
Robin (talk) 15:57, 19 November 2009 (UTC)
replies: text: Alright, agreed. Maybe if we end up listing only decision problems, that column can be taken out too. --Robin (talk) 14:33, 21 November 2009 (UTC)

text: OK, sounds reasonable. --Robin (talk) 15:38, 21 November 2009 (UTC)
thread_title:  Table or list? 

message: It is not good form to use the phrase, "one tries to keep"
"Even though some proofs of complexity-theoretic theorems regularly assume some concrete choice of input encoding, one tries to keep the discussion abstract enough to be independent of the choice of encoding. This can be achieved by ensuring that different representations can be transformed into each other efficiently.one tries to keep the discussion abstract enough to be independent of the choice of encoding. This can be achieved by ensuring that different representations can be transformed into each other efficiently."
Better might be,
"When considering complexity the problem should be presented in an abstract form, so that each concrete representation may be transformed into the same problem."  — Preceding unsigned comment added by Thepigdog (talk • contribs) 08:06, 12 October 2011 (UTC)
thread_title:  One says 

message: The supertask article has a note at the top stating "For the computer science term, see Computational complexity theory." Is that note accurate? Taken literally, it is not, as the term supertask cannot actually be found anywhere in this article. But I ask here because readers of this talk page may know if that characterization is somehow appropriate. Regards, Orange Suede Sofa (talk) 07:11, 23 October 2012 (UTC)
thread_title:  Supertasks 

message: Upper_and_lower_bounds_on_the_complexity_of_problems, begin with stating that "one is interested in proving upper and lower bounds on the minimum amount of time required by the most efficient algorithm solving a given problem. The complexity of an algorithm is usually taken to be its worst-case complexity" Shouldn't it be the maximum amount of time?--Natematic (talk) 17:55, 18 November 2012 (UTC)
replies: text: The complexity is the minimum time required, the running time of the most efficient algorithm.  It is possible to spend as much time as you like on solving a problem, so the maximum time isn't a useful concept -- although it can be thought-provoking, see Bogosort for example.  The worst case is the maximum of those minimum times, in other words the greatest length of time you can be compelled to spend even doing it as quickly as possible.  Deltahedron (talk) 18:26, 18 November 2012 (UTC)
replies: text: I agree with you. My point is: if you say "one is interested in proving upper and lower bounds on the minimum amount of time required by the most efficient algorithm solving a given problem", I get that considering the most efficient algorithm, you say that the complexity is the time it spend in its best-case. In other words, it seems to me that the best-fitting formalization for that proposition above is \min_{x\in X} \{time(T(x))\} where X is the set of possible input and T is the most efficient algorithm.  — Preceding unsigned comment added by Natematic (talk • contribs) 19:25, 18 November 2012 (UTC)
thread_title:  Computational complexity 

message: Why does the map showing the shortest route to visit 15 german cities,  only actually visit 14 of them ?Eregli bob (talk) 11:19, 11 May 2013 (UTC)
replies: text: You're right. Other sources also claim that this route covers 15 cities. For example, see . --Robin (talk) 19:14, 14 May 2013 (UTC)
replies: text: The answer to the mystery was one mouse click away. Instead of doing original research :-) The image description says that Dortmund is not labelled in the map (I guess because, as you can see it yourself, there is simply no place for it on the map, despite (or because of) being the largest city in Ruhr area :-) Staszek Lem (talk) 02:16, 12 May 2014 (UTC)
thread_title:  Dodgy Map 

message: We read
It is tempting to think that the notion of function problems is much richer than the notion of decision problems. However, this is not really the case, since function problems can be recast as decision problems. For example, the multiplication of two integers can be expressed as the set of triples (a, b, c) such that the relation a × b = c holds. Deciding whether a given triple is a member of this set corresponds to solving the problem of multiplying two numbers.
This does not sound correct at all. Consider the predicate "pfactors([f0...fn],composite)", which is TRUE if [f0...fn] are the prime factors of the composite. Evidently, the decision problem "pfactors([f0...fn],composite)" is MUCH easier than the function problem "pfactors([F0...Fn],composite)" where F0 ... Fn are variables to be determined and even n is unknown. Additionally, in the given example, there may be ways to check whether a x b = c holds much more easily than actually computing a x b (we just need to "fail fast" after all). Additionally, the text says "function problems can be recast as decision problems" and then proceeds to given an example where a decision problem is recast as a function problem...
See also for example FNP vs. NP : https://complexityzoo.uwaterloo.ca/Complexity_Zoo:F#fnp (which I don't quite understand yet) There is a T101 in your kitchen (talk) 21:46, 8 October 2016 (UTC)
thread_title:  Difference between "decision problems" and "function problems" 

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thread_title:  External links modified 

message: I will undo the change 03:53, 19 May 2018‎ of 69.172.150.202. The user removed the bold text from the following paragraph.
 
So the text was changed to
The user added the followind comment to justify the edit: 
The original text was brought to the attention of the user by me in a discussion of a  post at codereview.stackexchange.com. Ihe user than told me: 
(https://codereview.stackexchange.com/questions/194611/hackerrank-challenge-apple-and-orange#comment374709_194617)
 
and changed  this wiki text as described above.
 
The reason given for the change is nonsense. 
James Aspnes says in Notes on Computational Complexity Theory, CPSC 468/568: Spring 2017, page 7
 
So the size of the input depends on the alphabet used to encode the input of the turing machine but is proportional to the number of bits of the input numbers
Also  the Stanford Encyclopedia of Philosophy says
 
These are two citations for the original statement.
 
 
Miracle173 (talk) 22:01, 21 May 2018 (UTC)
replies: text: I agree with your addition. Input size is conventionally measured by the number of bits in the input. --Robin (talk) 06:29, 22 May 2018 (UTC)
thread_title: Input size

message: Under Computational problems -> Problem instances, it says quantitative answer, but all I see is a yes/no answer, where is the quantity in the answer?
I think quantitative should be removed, what do you guys think?  — Preceding unsigned comment added by Shalevku (talk • contribs) 16:31, 9 January 2020 (UTC)
thread_title:  The quantitative answer?