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P, NP and mathematics - a computational complexity perspective

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dis too date match that time BAGHDAD duos next week there aren't we beat their obtained he is a bachelor's degree from the neon in 1980 and from and BHP crown
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
but I think the most important aspect of his mathematical personality is is is extremely broad knowledge and is extremely broad view about what is going on any time you have any questions about what there is on that area really about time we will give you a fantastic description on going to the you would think there may be only after somebody's special person that Daddy would be obvious considers theoretical computer science as start mathematics that you which I chair and he has been thinking about working on some of these extremely difficult questions which many of which can be some arrives as a simple dichotomy like determine is versus non determinants all I want is relationship between Fatah repetition brought there's sequence repetition and proper or what is the relationship between now and the amputation amputation using randomness N vs. them if can get on it is with great expectation that I am looking forward to this Dole some so it's END and mathematics from the respect he wanted Nacional what's so I'll have a a look at the bureau must but Our we written something like that that the page blanked the beginning of the year by a locked with them from lectures from on my don't Bond on this very broad subject and those the man of the people topic folder docket it's about 1 hour however what they decide to do it talk about a man so but to what this is the talk of our views of the strength of the what's the adopted by a man in many Fulton bodies of mathematics but the trip but the key the only information about many view of the the Mets in mathematics but if it does the love there is immense and abandonment and the on the phone that advance of go on point of view of Islam as and computational complexity when no time most of them and other results turned you want the all-powerful 2 so that is what we have on the than the last 20 or years about this costs for months highlights of the summary of the top palette have review found that on of the complexity then what that means but them How the problems the Bureau that problem I have for months because it would be a century later the Terry speculated that the centuries later for the rest of the our In 2 pots of them played the powerful on the computation with examples for of the month for them and then I'll tell you why actually may not be what it seems and get us in understanding of the traditional forms on and the ovation from difficulty and that they were I want to talk about another set savings based in understanding the mother Kabul operators are we're going to start the complexity of computational Parsons the people of humanity always wanted to blow things efficiently our time on I'll bomb of but after doing gave the conditional can the became the mathematical object of the computers are complex problems to the bottom of the object of study and the Embudo examples famous examples and I want to use it to them of course is your heart that is a problem with the of great 2nd graders out lure long multiplication are we want to study of the functional the length of the data the length of the number comedies of the desirable rely on their bandages the modification from like and world that but that was before an easy for the poor normal time on that P is another problem with just there In most of the time IBM entered the final plant articles and Italy are not doing that might be the best not only the full father-son 1 and the growth the mambo they did it to its formula and if that was the best we could do this would be a problem for months I'm marvel at a very inefficient on the full of things we don't know whether how the town and the law and the thing here is that and the whole world including all of fuel buying and using your credit they don't believe that part because that's what the security of that section back about nevertheless we don't all that great challenge for it is another problem which is probably deal for everybody who saw the size professional thought still holding they bought what remains very much about the state of default choice hypothesis and some integer an ass commonly trade for big fooled Don over that some of those defined as a portfolio amenities system on the front of the lens 1 exists however the complexity of the problem and I think everybody would agree that in general will be difficult but we don't know that but we don't know relations between the complexity of problems for example it done the other that the 5 for this the far-flung of them fall fucked going in 3rd with no we don't know whether that is author of this in cage and is a consequence of a very basic who can learn from the seventies that COM problem is the that universal support the complete for them in the class that day was wanted defined the and last laugh and popular these in Comparex annual number also other programs form a month from computer fly from other sciences that look for the final leg of of the men's pleasure of what that for summer vision but that be better the last board of that and if you want to stay reverse them formal way which is just the amount of time would the fulfilled camachile over that and we don't know we don't get read on cannot put it out there and of course the capture of a much deeper thing that questions about whether we can automate PA David his mother mother creativity but that should much bigger than for that the question we cannot but we have our lives all the problems in and 3 and even beyond our forwards really don't have for now and plan on them we don't have anything on the the obvious financial I'm not going to be the best we can do so if you have the care if any of this problem any of the problems hardly while financial signed by the best exponents of flights by the
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 the bottom and the question then is the may available for what do you expect that they would not loaded will accept that the does the job with a very high probability that the United called for why should want always in Russia than it once did well our money on those in who the good will of the the best remember the truth already anyway in light of all the time so why not novel as the elves and for this account with the much better behaved denials in life you can leave them out of the woods something rule you just off the cliff and want to avoid being over time solubility coupled with Domenech Simon Taylor and of course the way the way that we it is for some problems we can and can't do it the domestically we'll and it's a very powerful tool examples want further it is No. away from my time and he'll give our communities similar talks for like when many of them a but might find examples but have the probabilistic solution but not that want but this warning the revealed by beautiful in the summer what I said what the problem is that I give you an N and and I asked whether Bryant our growth both brought to the island for ages Bob dollar for the most lives but laugh challenging the world find in the complex there's no complexity of With all in the language of France is talking about before he demurred company it's clear what laughter from the complexity of our this wall that the some of these often David probably forgot the the the age of publicity computation but efficient viable for that by Monday that but Marley and that this will be the best example and wonderful Wakefield about about the pool work our current would not follow the our so that's another example the type I wanted but the related 1 which is I don't think have the number for and Brian but politically but because of the density of blind just be with their father and line in general number of friends they did and applied to each of them by mother that work with that probability of 1 of them many of them the so the density don't bother France before the Chicago nobody and I'd be out of reach in the of fun so far so that's 1 example but an example from under Bush for now their identities of Vermont saying I want to but the wander make and viable look at the dominant in all them if earlier court for the before and from among the pool but I just want them to clarify the next 4 months of 5 object to open thought check on the coefficient little the freedom of the and you would never have thought but not the way the data from the better that sympathy over overnight but In general if I give you another button on the mouse something that you think if has money came up with related identity support not only of the died from our implicitly like this 1 and you want to know about whether it's identically premises completely I would do it our but again probabilistically it's very simple a simple Schroth things are going well and it will not not not identical then survived a measure want not the only and country renders the size enough big a value for each of the Bible blond only in the range of the city in 1 of the Honda B and did the same for each 1 you Puget Drive with very simple sampling and or from report on a rather than his daughter will always be able but if you not not identical you will get arms deal with the title of the simple and IBM nobody out Mr. Chretien Flaubert sponsored by the end of the of of course you may remain calm violators in Austria above the for the the wine and there's no that if you what but the problem is probably completes canceled find but are good but on the other direction if the food is not enough from Danish film and alumni is the degree of support on them could do much more than that they were our better on the value of the a place in the onto Bob packages you can't fight for long before and again for with garbage and has no obvious account of or OK a amount and my thoughts of everything so we're pretty positive again 4 and 5 guide lists like function on the tube on the boron and that's a member of formula and some Epsilon and you want to find all the La Jolla coefficient of the if they don't want to manage that man-made together at by the soul can you now In the Plymouth who example the account on militants but if it does sample blindly and what it was more sophisticated the beautiful for basic robot 11 which last adoptive sound and the which gets the see or lastly proficiency on and the effects can be extended to all the quality of billions will benefit from site I'll guarded and it is ready for the applications in accordance with complex and no way of doing and the last 1 geometry is garish red basic problem the problem is that your demands In the high-dimensional comics
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 bigger ball because of high demand the probability of forming in the body exponents of the small so what to do if something much more clever the data on the walking what for this is a flight for a lot of time with the that food take care on the wall inside the body and the issue just happened to move out to immediately go and amount of and its eventually will get to wear uniforms point in the a body but eventually gave them away and does not know show that you wanted to make sure that we're not trying to get and the Europe from wisest forget the Markov chain and for this the developing the met in it for its down from the body and that type of thing going for the schools should mention that marbles James Beard a lot of the Monte Carlo method the From McConnell but are lies in the belly of Markov chains the ball for me is that mixed and it's important will the only other order in so we've been following example of of believe order for Remele that on those around them held over the among the most plates or ignore or other problems that have reported their time on the way but all the delays to come with the 2nd fundamental problem and the below finance and the where only example than our common knowledge would attempt to conjecture on Thursday the net in mind the previous from the fundamental problem the event deal with the problems of acquired from until final than we also believe that so the mayor point of this lecture for both do not these they token gesture for or even tho they don't be late the ball intimately related fact 1 on the conduct of must and if you of week a so what what's going on what is the comment and what is coming for that's what I want went to in the next couple of flood again damage what what is our way of saying if there are hard problem on to knock the ball off from Earth the lives of the connection between how so that this this is evolved over except for along with additional want will be rid of mathematical may remember not stated the report 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would do whatever for the job as the uniform the what are the distribution of maybe by fall within called of the same on the without the computer what type and or the other is the definition of fundamental definition wanted it will have to to give it to let's call the distribution of food on the eve of the 5 exactly what we want is down from a heavily the official sort of way efficient on every will behave the same goal as the visitors although I'm not efficient what they can distinguish it from 1 that's the key the mission and once the conditions that you can buy the question is whether there is an awful on the list would be modeled on the uniform and whether you can build it without so that's exactly what we are trying to do under Creative along with the British without from the diplomacy to let me tell you so we're who want to create and
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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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 re-elected 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 soon-to-be 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 Wal-Mart 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 fourth-seeded 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 Wal-Mart which a fall this but
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 be-all 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 pre-eminent 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
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Metadaten

Formale Metadaten

Titel P, NP and mathematics - a computational complexity perspective
Serientitel International Congress of Mathematicians, Madrid 2006
Anzahl der Teile 33
Autor Wigderson, Avi
Lizenz CC-Namensnennung 3.0 Deutschland:
Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen.
DOI 10.5446/15981
Herausgeber Instituto de Ciencias Matemáticas (ICMAT)
Erscheinungsjahr 2006
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Mathematik
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.
Schlagwörter P
NP
computational complexity

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