P, NP and mathematics  a computational complexity perspective
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P, NP and mathematics  a computational complexity perspective

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Number of Parts 
33

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CC Attribution 3.0 Germany:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
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Release Date 
2006

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English

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Abstract 
The P versus NP question distinguished itself as the central question of theoretical computer science nearly four decades ago. The quest to resolve it, and more generally, to understand the power and limits of efficient computation, has led to the development of computational complexity theory. While this mathematical discipline in general, and the P vs. NP problem in particular, have gained prominence within the mathematics community in the past decade, it is still largely viewed as a problem of computer science.

Keywords  P NP computational complexity 
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Princeton University in 1983 on monkeys warrants I would like to mention just above price which he received a 19 94 army has many outstanding results are in the Theory of Computing gap theory and in other areas around I don't think of it as sign but beside these outstanding results what I would like to be
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best the Our Uribe's falls under of the sun in front of everybody lives and I'll be there for them now problems in and 3 life for you will require much of for that 1 fundamental question of whether the sign but may moved to the 2nd fundamental questions which is about the ball from the what they want to rule on the way by a few examples it is set problem very natural problems with the examples of for each of which we have a very efficient ballistic and for now we do we have a mammoth comic corners on the floor is weird them on like Powell a other examples from the front of the quantum optics with over basic simple the state program but before that just defined what the public to gobble up with them of the program that it is allowed only to prove that to 4 . 0 by our so we assumed the limit of although it just the traffic uniform distribution of the dependent on kind of we doublet and candles for the vision and Of course once you allow the computation the outcome of computation comes on 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object the different ways that reports of be run by the bombing type of plane and you want to estimate the volume of what the boardroom of all the now it because both out of fear the computing the modem exactly it is and wealth and promptly we should settle for an approximation of the were not program for long Simon the end of this year for White Bluff cameraman them but the people with more always find beautiful faster I with them similarly for a policy for the game the idea of ballistic for the damage would be fun the previous 1 of the highlights of the idea that coming the 1st thing is that the faithful from giving the boss of bosses may think about it laughter counting the number of books image counting the number not points inside the body and on the next is a collection of very basic connections between approximate accounting and uniform Sam it down would be sufficient to find them almost on point inside the body reports the count but now we cannot pull down general sampling the 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on the Web wait we can can she's something clear workers have just left this should the complexion of the and efficient because we want From reflection together the gift appears so we can keep them out of form no 1 will be performed a few on the wide because if we just let several Member on the eve of a friend is not a problem because we can't ignore the possibility a number possibilities Of course not for that's OK and I want to want Louis congress of the law that fuel independent bid on the big in the former for every possible the focus of visible run you do that and what the crumb action belong the for what may be real steps this what they called the the ball on the them and a few on the beach so the the on and thought we that on what we want our show it just north of Congress Janet world and the managed to on the bits of dust shortly after just in case the amount will be by 1 and have on the distribution how that if like they were I want getting on for this that the ball that this only we have to do make something that looks a lot the took some predictable checked 1 on the so well in the 1st period obviously just copying what we have tried multiple we have a problem before How do get demanded the last thing that should be looked and predictable when efficient computation our there is only 1 thing compare career of Libby's so we compare some functional and but should be computationally differs from visitors and they've got computers difficult thing than ever but not on this will not be able to predict the exactly from the previous month but we should not be able to get that of 50 50 because that's what I'm not to shut off they should be able but the 55th and so what we need is a long out of the habit of case function and what we have where your where the what we're doing something last week it would just as soon the problems are difficult maybe just on
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1 end and that the phone what to do in the final hour trip to find the difficulty of function that may be our on them as a function that problem essentially things if small question parents the best you can door and there's a lot frozen for this but the thing is that you can view of the problem on our conscience the computer would that be albeit that look around dawn but efficient but it chief of the food on the generous but just make sure that we understand that the whole what happened to the way we determined to be emulated Mr. cargo who will look at this generator we're just can't laughter and so why should we want without this otherwise we know what for now in many of the city's evaluated the article 3 on them and take advantage of a majority and this would be headed to now exactly the political will be mission now than we make upon William Paulson to about this this on the top of line we wanted to formal pool removal on
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the platform or possible rather than could do it under function on the list function that we have if a problem but they can't be but this farmland is much more possible powerful enough for example you may want to fool not all out of Dubai 1 I think a lot Ms. optical on finalizing around the in a particular way maybe you can just fully the yourself on the that and it does not that you can do it in a specific instance than some of the the highlights of the plan amounted to a thing of the deterministic lamented that they are with them the current success might wandered on my hip optical play Mali at and as low firms and similarly problem I'll talked about Chris know is so the lot of the title which is based on that difficulty you can computer from all of that so long as clean and that have behaved like Everett of old bundled with would let both tool the poll found that out competition that that thing is the very anxious problem is the taste of your time limit that but I'm always like to prompt they have all been said not believe want get your tell you have no matter and more over you have no memory in the sense that you cannot just Rowan down you it just family member basically what you are and what are the names of the streets of currently looking but that's all that's what we call locks based on what you to about Logan be sample and and 5 off that would be playing tomorrow if what do you have over what to do about of what got beautiful that is the thing that made off and me on what it should do just around the world are the main member while walking and maybe it is important not time you will get your what that and blackmail the hope that the auto before the director of like you're 1 we of that the rally down if it wasn't for this what Grant and this woman is not an isolated problem again it's a complete problem for Mets a colossal there's no problem and what the publicity guard with natural West can you it's a very different game motives fall and this is just the for last year amazing example of the deadly were talking with forms Is that you can replace the behavior by the basic law that do
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exactly that get to the altar of the city are and what can be computer that there's not a lot but remember ever received an even more remarkable is this inside he has In a week so the 1 that I have in the building is based on its bundle that same not reelected the because most do the not behind the the firm popped into them From selection on the laugh that we before the year's so for that product for its beautiful gotta due to growth stocks that's 1 in the face February with Theobald them IBM will run out of steam as far worse in about on the other 4 were floating around the soontobe or so far and be problem pop than the sum is done in the case of 2 Arab nominally but in this if Lara the last 1 I want to talk about the setting which is the Grand politically trust and about for what does Londoners will pull so I want to talk about political system most the same person who would buy pulp and paper goal mccurry of by the study what a political system that identify what the don't both of them is that if your not after we are with and forceful enclave whether be from model the claim that in my head we want what they do the statement and we want WalMart and what the world we in there from the complexity of all multiple systems in the market it they both system is defined by vilification things the cargo which would be efficient than or courses in mathematics of fish of course we expect to be able to verify it takes bar the claim and the other end of the obvious some the from is the claim and thus should be a convincing argument and that a good case in which case we call declined from the down from war everybody happy and on the other hand if the brand fault it would be nice volume and the economy of this the the strong so that the the normal course of them wanted the poll released forces out by the way notice in the in the nation the older players play out weekly mind what are some of them come up with but I do everywhere but the publicity for system well that this have is the same as before we want the claim but there is and what be wind opting for forces from sort that for what becomes of this is that the value of the rectification fourthseeded allowed on analog will make appears we are allowed make a more refined oil should be appalling mathematicians and suddenly you may not wanted we some of those above the but the even of that so from everyone already and we are willing to give up a little bit in the sound so it's possible but with extremely low probability that before but if I be convinced that the long claimed Hawaii where where where with the youth of the nation we thought we don't want it there may not want to go before they both be it to do all of our what they thought of that a lot political bosses and have the once don't what some remarkable properties of public and the about 2 kind that provide for the publicity to check a book pools of peacekeeping um which eventually under left the question the arrival the of voting cost and knowledge purported 2 against so what others do our political system for both of them and we have the use of such what works and what they might have a full role as the and report about a final want Turkey thanks in bold this year forces them the valley fire who wants vilified that the argument collects it is allowed just sample Honda B on the pool for the amount that can be fatal the we strongly but randomly selected bits of the argument that killed somebody decides whether it's in the of the thicket I mean we know that cannot kitchen but in the end before about the point about disagrees that the war would be optical of fashion make it useful and if remarkable is not at the bottom of the this people Evelyn Evelyn mathematical tools can become about the efficiently Philip B. being all WalMart which a fall this but
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notification with with me at all so if it would later fired because I think it would be fair to say that England would be much easier for Bolivia pot it would not however I want just less than that the competition is not from but they should for the Standing Committee of the optimization and approximation cargo from out of for and that's a very very powerful tool and the the last yield lives emaciated often on the standard of vision of their port to measure performance based on this the other magic the political posts River things that but now we are worried about it before the vote if I want to fight for now we comes down the pulled wanted the weather the weather you may be aware that if I were the published show what are the owners the competently ridiculous consequence of Fairfield because the pools which severely volley that collect of the state and the real absolutely nothing about the content of the it maybe because of the previous 1 but although before the year before Wetzel this also is that the orange Emily will forget that I will not allow Wolf candy from relatives of the Maoist former but if I had the all of the hypothesis frustrated if I could convince your freely without giving your of what's in them but you will be felt that I probably want there is a difference between these the previous day or and this is assuming 1 refund could feel the Fox told the Fox problems at the Jakarta and is in need invaded of the major application of plagiarism goes in pool people about big wave bit sentimental within the fold of the law all sorts of magical properties of portables about what the the place for that another thing of woefully out thanks knowledge in the Greek modification cannot be done if you have the both the if the butterfly leaving and toppled be OK that some of ice 1 1 thing that is was more general than this the hope is that no 1 in this computational complexity glasses and consider the efficiency of the port city involved all the efficiency of the but depends in part to corrupt a video on the Senate but because France then concepts change meaning actually sometimes get them for that to work around the has gained further the already the cool sold the remission of war lots more and brought about by the for which the that on the mission here is that it's in the eyes of others the followed Of the beall that God you hungry absolute don't be ran from outside Europe the study your on sequence and white wine bottle on computers and how can generate good enough with enough in the sense good enough for official biographer and duffel followed with a probably just got we another set of remedies sometimes cannot be eliminated the rather talk about with the the butt of computing and defeat them on and that's where we don't following is showing but did they said they fall even for this accountable exams the power line from the basic them off and just designed no favor for basic are them and then might get in the door forgot that some of the things we fans the substitute northern found we don't know our With outside declared depend on how we better find out where the loot for anthology how that 4 major the fundamental question No. 1 who rolled off the complexity of found what can we do it for fun maybe and really want to lower the from project not that former comments use of basic you aware of the by a basic from other funds is still unfolding of the real problem with toddlers we believe it is a different matter can creativity I already have this when I have that talk like we have a conversation with a mathematician about these admit they don't interfere soulful but and I love my poem about what what to blow they will time without the bag and get the ball in the dueling lashing out what how can a mathematician to confirm not the answer an dog my answer is there are now many ways Davis and or off you can work your work from the complete want particularly appealing some of which have not met Our from governments and doing it proliferation in the bought army of the vary from Middle School of our field make sure that could not to otherwise plus on tho favor functions the down on the amount of None of the admittedly of what you want to know that don't have the same function without them a sign that the border Wandiligong build opponent of and venerated it is 1 way you might want to never mind wife it 1 where you can go about you can buy the project the dominant so you can buy and bad and bandmates or allow them to abide by way of a fine match and that computer the down and out of the allowed and what you want that that would have allowed might be the parliament of the more flow but did not for a man will be found on the composition of the government to find them alive now get and the all of dearly can be done it can be done but let me give still 1 that can be done and the size of the karaoke financially late in life but to have a little bit of a total ban will fight the result body and soul for much some of the value and rolled on the best 1 the reasons why For the body on the role and work what do you do it doesn't go in for role on the Will they still upon an army out of the they different the relative concrete clearly are by questions maybe the lightweight world let question I put it in both because not exactly think about it don't the downtown the tournament on home programs a popular month like preeminent be slightly before and it supported them for finite the slow barnful fine if I feel that it pulled the bees from and the program for Internet fearful for the complex task of whatever right isn't a thing of Paul but thank you