tag:blogger.com,1999:blog-3722233Fri, 26 Aug 2016 02:58:26 +0000typecastfocs metacommentsComputational ComplexityComputational Complexity and other fun stuff in math and computer science from Lance Fortnow and Bill Gasarchhttp://blog.computationalcomplexity.org/noreply@blogger.com (Lance Fortnow)Blogger2408125tag:blogger.com,1999:blog-3722233.post-8389761393648100882Thu, 25 Aug 2016 13:32:00 +00002016-08-25T09:34:54.869-04:001956 Was a Fine VintageBill sends me an email last week with the subject "Our field is getting old!" and talks about upcoming 60th birthday/retirement conferences he's invited to, all of which I've been invited to as well. Bill's subject line should have read "We're getting old."<br />
<br />
Here's what's upcoming:<br />
<ul>
<li>Avi Wigderson's <a href="https://www.math.ias.edu/avi60">60th celebration</a> before <a href="http://dimacs.rutgers.edu/FOCS16/">FOCS</a> in New Jersey, October 5-8. Avi is a giant in computational complexity and the event has an amazing line-up of speakers.</li>
<li>Albert Meyer's <a href="http://people.csail.mit.edu/afadli">retirement celebration</a> at MIT, November 11. </li>
<li>Rod Downey's <a href="http://sms.victoria.ac.nz/Events/CCS2017/WebHome">60th symposium</a> in New Zealand, January 5-8.</li>
<li>Eric Allender and Michael Saks will have a joint 60th celebration at DIMACS in New Jersey, January 26-27.</li>
</ul>
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Surely I've missed some. Feel free to add in the comments.</div>
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Theoretical computer science has a tradition of holding a symposium in honor of a 60th birthday, typically organized by the PhD students. I co-organized such a <a href="http://math.mit.edu/conferences/sipser/">celebration</a> for my advisor Michael Sipser two years ago. 60 is a good age, a time to look back but not quite the end of a career. </div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-AxGiATLuFz4/V73tThrxtUI/AAAAAAABXJ0/5DtE0ZU5y-8kcA-sorYZqiBcHHzffE5CwCLcB/s1600/Hartmanis.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="231" src="https://2.bp.blogspot.com/-AxGiATLuFz4/V73tThrxtUI/AAAAAAABXJ0/5DtE0ZU5y-8kcA-sorYZqiBcHHzffE5CwCLcB/s320/Hartmanis.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Janos Simon giving toast to Juris Hartmanis (center).</td></tr>
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The first 60th I attended was for Juris Hartmanis, one of the founders of computational complexity, back in 1988 at the 3rd Structure in Complexity Theory (now Computational Complexity Conference) meeting in DC. The conference announcement required everyone to where a jacket and tie, the first and probably last time I will see a bunch of complexity theorists all dressed up.</div>
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Juris was also the first faculty retirement I attended in 2001 at Cornell. Retirement celebrations are generally organized by the department.</div>
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Many of the first generation of CS theorists from the 60's and 70's are hitting retirement age. The 1980s saw an explosion in CS theory PhDs and many of them turn 60 in the near future. Expects lots of celebrations, great speakers and remembering many great careers. </div>
http://blog.computationalcomplexity.org/2016/08/1956-was-fine-vintage.htmlnoreply@blogger.com (Lance Fortnow)2tag:blogger.com,1999:blog-3722233.post-548110834624852686Mon, 22 Aug 2016 20:25:00 +00002016-08-22T16:25:25.027-04:00Chrisitan Comment on the Jesus Wife Thing misses the important pointIn 2012 a Professor of Divisinity at Harvard, Karen King, announced that she had a fragment that seemed to indicate that Jesus had a wife. It was later found to be fake. The article that really showed it was a fake was in the Atlantic monthly <a href="http://www.theatlantic.com/magazine/archive/2016/07/the-unbelievable-tale-of-jesus-wife/485573/">here</a>. A Christian Publication called Breakpoint told the story: <a href="http://www.christianheadlines.com/columnists/breakpoint/gospel-of-jesus-wife-found-to-be-fake.html">here</a>.<br />
<br />
When I read a story about person X being proven wrong the question upper most in my mind is: <i>how did X react? </i>If they retract then they still have my respect and can keep on doing whatever work they were doing. If they dig in their heels and insist they are still right, or that a minor fix will make the proof correct (more common in our area than in history) then they lose all my respect.<br />
<br />
The tenth paragraph has the following:<br />
<br />
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<i>Within days of the article’s publication, King admitted that the fragment is probably a forgery. Even more damaging, she told Sabar that “I haven’t engaged the provenance questions at all” and that she was “not particularly” interested in what he had discovered.</i></div>
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<br />
<br />
Dr. King should have been more careful and more curious (though hindsight is wonderful) initially. However, her admitting it was probably a forgery (probably?) is ... okay. I wish she was more definite in her admission but... I've seen far worse.<br />
<br />
A good scholar will admit when they are wrong. A good scholar will look at the evidence and be prepared to change their minds.<br />
<br />
Does Breakpoint itself do this when discussing <a href="http://www.breakpoint.org/bpcommentaries/entry/13/28370">homosexuality</a> or <a href="http://www.breakpoint.org/features-columns/articles/entry/12/9574">evolution</a> or <a href="http://www.breakpoint.org/bpcommentaries/entry/13/23530">global warming</a>. I leave that to the reader.<br />
<br />
However, my major point is that the difference between a serious scientist and a crank is what one does when confronted with evidence that you are wrong.<br />
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http://blog.computationalcomplexity.org/2016/08/chrisitan-comment-on-jesus-wife-thing.htmlnoreply@blogger.com (GASARCH)2tag:blogger.com,1999:blog-3722233.post-4003504497082287633Thu, 18 Aug 2016 14:35:00 +00002016-08-18T10:35:07.606-04:00Predicting in Changing Environments<div class="tr_bq">
The New York Times yesterday <a href="http://www.nytimes.com/2016/08/17/us/climate-change-louisiana.html">ran a story</a> connecting climate change to the Louisiana flooding.</div>
<blockquote>
The National Weather Service reports that parts of Louisiana have received as much as 31 inches of rain in the last week, a number Dr. Easterling called “pretty staggering,” and one that exceeds an amount of precipitation that his center predicts will occur once every thousand years in the area.<br />Dr. Easterling said that those sorts of estimates were predicated on the idea that the climate was stable, a principle that has become outdated.<br />The third National Climate Assessment, released in 2014 by the United States Global Change Research Program, showed that “the amount of rain falling in very heavy precipitation events” had been significantly above average since 1991.<br />However, the research did not identify the South as one of the areas of greatest concern; the increase was found to be greatest in the Northeast, Midwest and Upper Great Plains regions of the United States.</blockquote>
In short climate change means our old prediction models of the weather no longer apply. On top of that, new models that tried to take into account climate change predicted heavier rains but not in that area of the country.<br />
<br />
The weather is hardly the only predictions gone bad this year. From Nate Cohn's <a href="http://www.nytimes.com/2016/05/05/upshot/what-i-got-wrong-about-donald-trump.html">What I Got Wrong About Donald Trump</a><br />
<blockquote>
Did he have a 1 percent chance to win when he descended the escalator of Trump Tower last June? Twenty percent? Or should we have known all along?<br />Was Mr. Trump’s [republican nomination] victory a black swan, the electoral equivalent of World War I or the Depression: an unlikely event with complex causes, some understood at the time but others overlooked, that came together in unexpected ways to produce a result that no one could have reasonably anticipated?<br />Or did we simply underestimate Mr. Trump from the start? Did we discount him because we assumed that voters would never nominate a reality-TV star for president, let alone a provocateur with iconoclastic policy views like his? Did we put too much stock in “the party decides,” a theory about the role of party elites in influencing the outcome of the primary process?<br />The answer, as best I can tell, is all of the above.<br />I do think we — and specifically, I — underestimated Mr. Trump. There were bad assumptions, misinterpretations of the data, and missed connections all along the way.</blockquote>
We also had bad predictions on Brexit and one factor in the 2008 financial crisis was a heavy reliance on historical patterns of housing prices.<br />
<br />
We have at our fingertips incredible prediction tools from machine learning models to prediction markets. Not all things change, our models trained to recognize cat pictures will continue to recognize cat pictures for a long time running. But as we continue to rely more and more on data driven predictions and decisions, be prepared for more and more surprises as underlying changes in the environmental, political and financial climates can pull the rug out from under us.http://blog.computationalcomplexity.org/2016/08/predicting-in-changing-environments.htmlnoreply@blogger.com (Lance Fortnow)1tag:blogger.com,1999:blog-3722233.post-3750682519448148391Mon, 15 Aug 2016 21:22:00 +00002016-08-15T17:22:15.441-04:00Is the examiner being pedantic? Whats really going on here?The following are two real conversations. For each one: (1) Is the examiner correct?, and<br />
(2) Where and when do you think this conversation took place?<br />
<br />
I give the answers below so you may want to read, stop and think, and then read on.<br />
<br />
CONVERSATION ONE:<br />
<br />
EXAMINER: What is the definition of a circle?<br />
<br />
STUDENT: The set of points equidistant from a given point.<br />
<br />
EXAMINER: Wrong! It is the set of ALL points equidistant from to a given point.<br />
<br />
CONVERSATION TWO:<br />
<br />
EXAMINER: What is the definition of a circle?<br />
<br />
STUDENT: It is the set of all points equidistant from a given point.<br />
<br />
EXAMINER: WRONG! You did not specify that the distance is nonzero.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
AN ANSWER I HAVE HEARD FROM SOME NON-MATHEMATICIANS: Since math people are pedantic and formal to an absurd level the examiner is correct.<br />
<br />
REAL ANSWER: Nobody in math would be that pedantic. In the old USSR, entrance exams for<br />
Moscow State University were rigged so that Jewish students could not pass. The following is a quote from<br />
<br />
<br />
<i>Bella Abramovna Subbbotovskaya and the Jewish People's university</i>, By G. Szpiro. Notices of the AMS Vol 54, . 1326--1330. <a href="http://www.ams.org/notices/200710/tx071001326p.pdf">Article is here</a><br />
<br />
<br />
The first story in it happened to Edward Frenkel when he was a 16-year-old taking the oral entrance exam to Moscow State University in 1984, recounted in his book Love and Mathematics, which I reviewed <a href="http://www.cs.umd.edu/~gasarch/BLOGPAPERS/lovemath.pdf">here</a>.<br />
<br />
<br />
BEGIN QUOTE<br />
Jews -- or applicants with Jewish-sounding names -- were singled out for special treatment. On one occasion a candidate was failed for answering the question <i>what is the definition of a circle </i>with<br />
<i>the set of points equidistant to a give point</i>. The correct answer, the examiner said, was t<i>he set of all</i> <i>points equidistant to a given point</i>. On another occasion an answer to the same question was deemed incorrect because the candidate had failed to stipulate that the distance had to be nonzero.<br />
END QUOTE<br />
<br />
A different technique used on the entrance exams was to give Jewish students problems that had simple solutions which were extremely difficult to find. The simplicity of the solution made appeals and complaints difficult. Some of these problems and their history is in this article:<br />
<br />
<i>Killer Problems </i>by Tanya Khovanova and Alexey Radul, The American Mathematical Monthly ,Vol 119, pp. 815--829.<a href="https://arxiv.org/abs/1110.1556">Article is here</a> (link is to arxiv version where title is<i> Jewish Problems</i>.)<br />
<br />
This is of course apalling; however, I have another issue to raise. Not allowing some part of your population to contribute is just... idiotic. What I really want to know is why did they do this when it so clearly worked against their interests. How would an<i> intelligent </i>defender of this system defend it? By intelligent I mean someone who knows that Jews are not FILL IN ANY FALSE NEGATIVE BELIEF ABOUT JEWS. By intelligent I also mean someone who actually sees the downside. In other words, how would they fill in the following sentence:<br />
<br />
<br />
The downside is that people who are talented in math and other fields do not get to contribute to our society, but the upside is FILL IN THE BLANK.<br />
<br />
For more information on this, but not really an answer to my question, see the Wikipedia entry on anti-semitism in Russia <a href="https://en.wikipedia.org/wiki/Antisemitism_in_Russia">here.</a><br />
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http://blog.computationalcomplexity.org/2016/08/is-examiner-being-pedantic-whats-really.htmlnoreply@blogger.com (GASARCH)6tag:blogger.com,1999:blog-3722233.post-8060885400119606304Thu, 11 Aug 2016 13:20:00 +00002016-08-11T09:20:19.454-04:00Robin Hanson's EmsRobin Hanson an economist at George Mason and author of the <a href="http://www.overcomingbias.com/">Overcoming Bias</a> blog, has a new book <a href="http://ageofem.com/">The Age of Em: Work, Love and Life when Robots Rule the Earth</a>. Em stands for brain emulation, a computerized version of a human brain processes including consciousness, all the wants, desires and faults of a human brain. An em can be created by copying from a human brain or another em, it can be stored and restored, slightly tweaked and can run faster or slower depending on the power consumption. Reminds me a bit of the cookies in the <a href="https://en.wikipedia.org/wiki/White_Christmas_(Black_Mirror)">White Christmas</a> episode of Black Mirror. Hanson also talks about clans, the collection of all the ems that descend from a particular human.<br />
<br />
The book has two distinct parts. The first gives a plausible physical and social explanation as to how and why the em world will come to be. Hanson gives the odds of such a world developing at one in a thousand. I put the odds much lower, especially since we have no true understanding of consciousness. For example if consciousness requires quantum entanglement, we would have no hope of copying into an em without destroying the old em (or human) it came from. More likely I expect we would have em-like machines that can perform a number of human-like tasks but won't have any true consciousness. Nevertheless I'd acknowledge that Hanson's world is at least possible given our current knowledge of the brain.<br />
<br />
I enjoyed more Hanson's discussion about the world of the ems given that they exist. Hanson takes a science, as opposed to a science fiction, approach to the topic, carefully thinking about how ems would work as a clan, how they interact politically, socially and economically. You can see the variety of topics in the table of contents on the book's <a href="http://ageofem.com/">website</a>. For example, Hanson argues that it makes economic sense to have ems split off as "spurs" to do more menial tasks in parallel in exchange for a short working life, as short as a few minutes, and a long retirement, with the retirement in a slower low-powered mode. Hanson has done some strong research and advocating for prediction markets (we even have a <a href="http://doi.org/10.1007/s00453-009-9323-2">joint paper</a> on the topic) that there is no surprise that markets show up as a decision making systems for ems.<br />
<br />
I don't agree with all of Hanson's conclusions, in particular he expects a certain rationality from ems that we don't often see in humans, and if ems are just human emulations, they may not want a short life and long retirement. Perhaps this book isn't about ems and robots at all, but about Hanson's vision of human-like creatures as true economic beings as he espouses in his blog. Not sure it is a world I'd like to be a part of, but it's a fascinating world nevertheless.http://blog.computationalcomplexity.org/2016/08/robin-hansons-ems.htmlnoreply@blogger.com (Lance Fortnow)3tag:blogger.com,1999:blog-3722233.post-6460197837409090916Mon, 08 Aug 2016 01:46:00 +00002016-08-07T21:46:40.587-04:00A Game Theory Conference! That sounds like fun!<br />
Bill: Lance just came back from <a href="http://www.games2016.nl/">Games</a>, a conference on Game Theory.<br />
<br />
Darling: That sound like fun! From what you tell me there is some nice math behind<br />
Monopoly(see <a href="http://www.math.uiuc.edu/~bishop/monopoly.pdf">here</a> for a paper on Monopoly as a Markov Process), Risk (see <a href="http://www4.stat.ncsu.edu/~jaosborn/research/RISK.pdf">here</a> for a paper on using Markov chains in the game Risk. Was Markov a game player?) and other FUN games.<br />
<br />
Bill: Uh, I don't think they talked much about those kinds of games.<br />
<br />
Darling: Darn. Did they talk about those really boring math games like Dup-Spoiler games, those games that AD is about, Gale-Stewart Games, Banach-Mazur games, Martingales, Pebble games, Communication complexity games. Oh, and Combinatorial games like NIM which can be sort of fun.Or did they talk about computers that play Chess and similar games? Or did they have talks on things like Chess being EXPTIME complete. Or did they talk about the Unique Game Conjecture.<br />
<br />
Bill: Most of the talks were about setting up a system so that all players acting in their own best interest is also good for the system. Like an auction system where it is a players best interest to bid what they actually think the item is worth.<br />
<br />
Darling: So there are no Games at a Game Theory conference?<br />
<br />
Bill: There were a few papers on Poker, but that's it.<br />
<br />
Darling: They should change the name of the field.<br />
<br />
Bill: Lance tells me that Ehud Kalai has suggested <i>Game Science. </i><br />
<i><br /></i>
Darling: So long as the word<i> Game</i> is in the title they should have fun games there. Oh well.<br />
<br />
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<br />http://blog.computationalcomplexity.org/2016/08/a-game-theory-conference-that-sounds.htmlnoreply@blogger.com (GASARCH)4tag:blogger.com,1999:blog-3722233.post-759307491572556180Wed, 03 Aug 2016 14:34:00 +00002016-08-03T10:34:45.956-04:00Seymour Papert (1928-2016)<div class="separator" style="clear: both; text-align: center;">
<a href="https://upload.wikimedia.org/wikipedia/commons/2/2c/Remi_turtlegrafik.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="200" src="https://upload.wikimedia.org/wikipedia/commons/2/2c/Remi_turtlegrafik.png" width="200" /></a></div>
Seymour Papert, the great AI pioneer, <a href="http://www.nytimes.com/2016/08/02/technology/seymour-papert-88-dies-saw-educations-future-in-computers.html">passed away Sunday</a> at the age of 88. In the theory community we best know him for his 1969 book <a href="https://books.google.com/books?id=U-O9BHlTvJIC">Perceptrons</a> with Marvin Minsky, who <a href="http://www.nytimes.com/2016/01/26/business/marvin-minsky-pioneer-in-artificial-intelligence-dies-at-88.html">died earlier this year</a>. In that book they show that a perceptron (what we now call a weighted threshold function) cannot compute parity, one of the first examples of a circuit lower bound.<br />
<br />
In the summer of 1982 I worked a a computer camp in Los Olivos, California and we taught the kids programming with the Logo programming language, a simple functional language co-created by Papert and Wally Feurzeig. In <a href="https://en.wikipedia.org/wiki/Logo_(programming_language)">Logo</a> you controlled a virtual turtle that carried a pen and you could give simple instructions like raising and lowering the pen, moving forward and backward and turning. With simple functions one could create complex diagrams, like the one above. Normally you would see the diagrams on a screen but we also had a physical electronic turtle that would move and draw on a sheet of paper. The kids loved it since they could see the results of their programs as a picture while they learn programming functions and recursion without realizing it.<br />
<br />
You can play with Logo at <a href="https://turtleacademy.com/">Turtle Academy</a> Logo set the stage for control of actors in many other computer languages designed for children including the tasks for the popular <a href="https://code.org/learn">Hour of Code</a>.<br />
<br />
Let's raise our turtle pens to honor Papert and the many that he brought into the world of computing.http://blog.computationalcomplexity.org/2016/08/seymour-papert-1928-2016.htmlnoreply@blogger.com (Lance Fortnow)2tag:blogger.com,1999:blog-3722233.post-6924534490549769325Thu, 28 Jul 2016 05:55:00 +00002016-07-28T01:55:49.662-04:00GAMES/EC 2016This week I report from Maastricht in the Netherlands from the <a href="http://www.games2016.nl/">GAMES 2016</a>, the 5th World Congress of the Game Theory Society. By having their congress every four years, everyone who is anyone in the game theory community makes a strong effort to be here, including three Nobel laureates, Robert Aumann, Roger Myerson and Eric Maskin. The conference has about 750 participants and up to 19 parallel sessions.<br />
<br />
This year the conference is co-located with the <a href="http://www.sigecom.org/ec16/">Economics and Computation</a> conference that comes more from the CS community. By co-located we are sharing the same buildings and many of the events, effectively one larger conference (which means in reality 21 parallel sessions).<br />
<br />
EC keeps growing, accepting 80 papers out of 242 submissions, all of which are freely <a href="http://www.sigecom.org/ec16/toc.html">downloadable</a>.<br />
<br />
My favorite EC talk was the best student paper, Deferred Acceptance with Compensation Chains by<br />
Piotr Dworczak, a graduate student in the Stanford Business School. He gives an algorithm for finding stable matchings with the property that every stable matching can be found by changing the order that the agents get to choose. The paper Which Is the Fairest (Rent Division) of Them All? by<br />
Kobi Gal, Moshe Mash, Ariel Procaccia and Yair Zick won best paper.<br />
<br />
Also a shout out to the talk Cadet-Branch Matching in a Quasi-Linear Labor Market solely authored by Ravi Jagadeesan, a rising junior undergraduate at Harvard. I went to grad school with Ravi's mother Lalita, and yes that makes me feel old.<br />
<br />
Tim Roughgarden gave the Kalai prize talk for his work on <a href="http://dx.doi.org/10.1145/1536414.1536485">Intrinsic Robustness of the Price of Anarchy</a>. The talk, attended by a good number of the game theorists, gave a general approach to generalizing bounds price of anarchy results to broader classes of equilibria. Tim followed Keith Chen who heads the analytic team for Uber and discussed how game theory and optimization ideas are driving a major e-commerce company. No major surprises but here's one trade secret: Uber covers its maps with hexagons while Lyft uses squares.<br />
<br />
All is all a great week, with packed schedules and crowded activities, but great to see all these game theorists and computer scientists talking with each other.http://blog.computationalcomplexity.org/2016/07/gamesec-2016.htmlnoreply@blogger.com (Lance Fortnow)0tag:blogger.com,1999:blog-3722233.post-3826854566236793594Mon, 25 Jul 2016 03:34:00 +00002016-07-24T23:34:21.081-04:00The College Issues that are talked about/College issues that are importantThe following college issues get lots of attention:<br />
<br />
Admissions- high school students PLAN to do things JUST to get them into an elite college. For example nobody takes the SATs just for the fun of it anymore.<br />
<br />
Admissions- Some High School Students are stressed out about college admissions, see <a href="http://www.nytimes.com/2016/04/21/us/greater-competition-for-college-places-means-higher-anxiety-too.html">here</a><br />
<br />
Admissions- Affirmative action.<br />
<br />
Admission- Lower standards for athletes?<br />
<br />
Sports- too much money spend on it?<br />
<br />
Sports- the players treated unfairly?<br />
<br />
Are other out-of-class activites also an issue? See <a href="http://www.thecrimson.com/article/2016/4/20/UC-revokes-group-funding/">here</a>.<br />
<br />
Jock Culture.<br />
<br />
Free speech- Speech codes, triggers. (I've heard this talked about for about 30 years now.)<br />
<br />
A common core. How to make it not just dead white males.<br />
<br />
A common core. How to get this to work when profs are overly specialized.<br />
<br />
Professors are rewarded for research more than teaching- how to induce them to be better teachers.(I've heard about this one for about 40 years.)<br />
<br />
Renaming buildings that are named after racists. ( Byrd Stadium at UMCP is now Maryland Stadium <a href="http://www.baltimoresun.com/news/maryland/bs-md-byrd-stadium-vote-20151211-story.html">see here</a>) (If we find out that Fields or Abel was a racist will we rename the awards? Why bother naming things after Justice Scalia or Bobby Kennedy when they will be renamed at some point because of their views on gay people?)<br />
<br />
Renaming buildings that are named after the things racists do (see <a href="http://www.nbcphiladelphia.com/news/local/Pennsylvania-College-Building-Lynch-Memorial-Hall-Racial-Overtunes-Lynch-Clyde-A-Lynch-Lebanon-Valley-College-361200551.html">here</a>)<br />
<br />
White privilege (If I was black then whenever my blog had bad spelling or grammar it would be connected to my race and assumed upbringing.)<br />
<br />
The crushing debts of $100,000 or so that some students face after college. (Which is why some students Feel the Bern!, though others Feel the Bern! for different reasons.)<br />
<br />
Hookup culture on campus<br />
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Lack of diversity in some majors (I've heard this talked about for about 30 years now.)<br />
(Examples: Across the country CS is at around 15% female. Art History is around 80% female. Why does the CS one generate much discussion and some outrage but the art history one... not so much? I would guess jobs. But the point of this list is just that these are the issues people ARE talking about.)<br />
<br />
Should college be vocational vs intellectual? Are these two disjoint?<br />
<br />
MOOCS: How will they affect education?<br />
<br />
These are important issues. But they affect few people. 65% (and dropping) high school seniors goto college. Over 1/2 of all college students go to community college. Many of those students are part timers who also work. Speech codes are not at the top of the things they have to worry about. These people face other problems that do not get attention. See the following excellent articles<br />
<br />
<a href="http://fivethirtyeight.com/features/shut-up-about-harvard/">Shut up abour Harvard</a> by Ben Cassleman<br />
<br />
and<br />
<br />
<a href="https://www.researchgate.net/publication/259452300_The_Other_75_College_Education_Beyond_the_Elite">The other 75%</a> by Paul Attewell and David Lavin<br />
<br />
To give one example: The number of students going to community college who need to take part time jobs to finish and end up with a crushing (to them) debt of $10,000 is a far more common problem then any of the ones above. Why so little coverage?<br />
<br />
The articles give other examples of problems that are NOT being talked about.<br />
<br />
The other 75% is from the excellent book <a href="http://www.amazon.com/College-Public-Purpose-Higher-Education/dp/0807752754">What is college for</a> edited by Lagemann and Lewis, and reviewed by me, for SIGACT News, <a href="https://www.cs.umd.edu/users/gasarch/BLOGPAPERS/college.pdf">here</a>. Most of the other chapters are about the issues above. We need a book, or at least a conversation, about issues of education affecting many more people.<br />
<br />
The <a href="https://en.wikipedia.org/wiki/Morrill_Land-Grant_Acts">Morrill Land-Grant Acts</a> established many colleges. It was passed in a time when it was realized that its important to have an educated public. It must have been passed in a time where there were not the pressing issues we have today (like bathrooms for transgender people) so they could think about these issues clearly. It was passed in 1862 <i>in the middle of the Civil War.</i><br />
<i><br /></i>
A meta-thought--- Every comment on this blog about the issues I list above as NOT affecting that many people will prove my point that those issues are discussed far more than issues that affect far more people. Even so, feel free to comment on whatever issues you want.http://blog.computationalcomplexity.org/2016/07/the-college-issues-that-are-talked.htmlnoreply@blogger.com (GASARCH)5tag:blogger.com,1999:blog-3722233.post-6458313013557172507Thu, 21 Jul 2016 12:33:00 +00002016-07-21T08:33:48.761-04:00Snowbird 2016Earlier this week I attended the <a href="http://cra.org/events/snowbird-2016/#agenda">2016 CRA Snowbird Conference</a>, a biennial meeting of CS chairs and other leaders in the the computing community. I’ve attended every meeting since 2010, the first as a panelists on journals in CS and the last three as department chair. I enjoy this meeting mostly for the networking with other chairs across the whole CS discipline.<br />
<br />
Computer science sits in an enviable position with booming enrollments, our graduates easily finding quality jobs in the field and computing literally changing society. Success breeds challenges, top of this list is how do we cover the dramatically increasing course load. Right now most schools are applying a variety of short-term solutions from increased use of larger classrooms, sometimes with recorded video, instructors and teaching faculty, PhD, MS and undergrad TAs and less small specialized graduate classes to allow for more core courses. What we haven’t seen is increased teaching loads. We need to be careful not to drive faculty into industry’s waiting arms.<br />
<br />
The confrence had some interesting speakers such as John Markoff from the New York Times on the excitement and concerns over machine learning and automation, Cynthia Dwork on the theory approach to privacy and fairness in the big data era, and Robert Morse from US News on how they rank CS departments. I'm generally fine with the US News Ranking, they measure reputation and reputation is in the end what matters in recruiting students and faculty. Many at the meeting had other, less friendly, opinions towards US News and rankings in general.<br />
<br />
One popular session discussed schools and colleges of computing beyond the department. Most of the successful transitions came out of CS programs in colleges of science, such as at CMU and Georgia Tech. Rarely do we see the transition out of engineering. With both the growth of computer science and its increasingly central role in many academic disciplines, now is a good time to make the argument for more colleges of computing. Perversely the growth makes such changes more challenging as an engineering dean would not want to give up such a large and growing part of their college.<br />
<br />
The Snowbird conference moves the conversation away from the weeds of current results to look back at what our field has achieved and where it is going. It's never been a more exciting time to be a computer scientist and while chairs always love to grumble when we get together, we all know how lucky we are to be leaders in this era.http://blog.computationalcomplexity.org/2016/07/snowbird-2016.htmlnoreply@blogger.com (Lance Fortnow)2tag:blogger.com,1999:blog-3722233.post-8773596742691138566Mon, 18 Jul 2016 12:06:00 +00002016-08-22T16:20:32.810-04:00Solution to the Alice-Bob-Box problem. In my <a href="http://blog.computationalcomplexity.org/2016/07/solution-to-infinite-hat-problema.html">last blog</a> I solved one problem and asked another (when will it end!). Damien Roberts provided an answer in the comments to the last blog, so kudos to Damien! I summarize the question asked and answer it (same answer as Damien, though more long winded) and then some comments and further questions.<br />
<br />
Peter Winkler told me this problem at the Joel Spencer 70th Bday conference. He got it from Sergui Hart who does not claim to be the inventor of it.<br />
<br />
PROBLEM:<br />
Alice and Bob play the following (non-fun) game:<br />
<br />
Alice puts natural numbers in the boxes 1,2,3,4,... She can put any number in any box. She can put the number 12 in two boxes. She can refuse to put primes in any box. The world is her burito!<br />
<br />
Bob opens all but a finite number of boxes. He chooses one of the boxes that is NOT opened and guesses what is in it and then opens it. If his guess is correct he wins! (not clear what he wins, but he wins).If not he is, as one of our candidates for prez would say, a LOOOOOOOSER.<br />
<br />
Would you rather be Alice or Bob?<br />
END OF PROBLEM<br />
<br />
(Added Later- below is an answer that I believe to be correct. Some people disagree. See some of the comments below and also the comments on <a href="http://mathoverflow.net/questions/151286/probabilities-in-a-riddle-involving-axiom-of-choice">this</a>)<br />
<br />
ANSWER:<br />
I would rather be Bob:<br />
<br />
As you might have guessed, Bob takes the set of all infinite sequences of natural numbers and looks at the equivalence x==y iff x and y differ on only a finite number of positions. He then picks a representative from each part of the induced partition.<br />
<br />
(When I tried to solve the problem thats as far as I got. Some commenters thought that was the solution, or the solution was obvious from that point. I don't see how.)<br />
<br />
Here is what Bob does;<br />
<br />
STEP 1: (I used to have Bob takes a random perm of the naturals and relabels the boxes but commenters pointed out that this was not needed and might not even make sense. So there is no Step 1, but I keep<br />
it in case someone sees this post and wonders what happened to step 1.)<br />
<br />
STEP2: Bob rearranges the boxes into (say) 100 rows. We'll say<br />
<br />
ROW1: BOXES: 1,101,201,301,...<br />
<br />
ROW2: BOXES: 2,102,202,302,...<br />
...<br />
ROW100: BOXES: 100,200,300,...<br />
<br />
STEP3: Bob picks a Row AT RANDOM (second use of probability). We will say ROW8:<br />
<br />
STEP4: Bob opens the boxes in all of the rows EXCEPT ROW8 (he will open some in ROW8 later). For each Row i NE 8 he does the following:<br />
<br />
ROWi is in one of the parts of the partition. Bob had ahead of time chosen a representative in that part. Let x(i) be such that from the x(i)th element on ROWi and the Representative AGREE.<br />
<br />
Let x = max of the x(i).<br />
<br />
So, for all rows i NE 8, if you look past the xth position, ROWi and the represenative for that equivalance class are the same.<br />
<br />
STEP5: Bob opens up, in ROW8, the boxes x+2, x+3,...<br />
<br />
STEP6: Bob knows the part that ROW8 is in the partition. Bob looks at the representative. Bob guesses that the number in box x+1 of ROW8 is the same as the number in the (x+1)th position of the representative.<br />
<br />
WHY is this a good idea?<br />
<br />
Consider ROWi. Let x(i) (as above) be such that past x(i) ROWi agrees with its rep. In order for the guess to be wrong you would need x(8) > all other x(i). How likely is that? Since we began with a random perm, the prob that x(8) is the largest (for that matter, the prob that any particular i_o has max x(i_0) ) is 1/100. So Bob wins with prob 1- 1/100<br />
<br />
Bob can do even better with 1000 rows or 10,000 rows, etc. For any eps>0 he can make the prob that he'll win 1-eps.<br />
END OF ANSWER<br />
<br />
One issue I've been trying to get at in this post and the last one was, is this a real solution? I think so, but some students don't like it. Even those that understand it. What do you think?<br />
<br />
There is no deterministic solution to the Alice-Bob-Box problem since if the adversary knows what box Bob will guess he can make it so that Bob gets it wrong.<br />
<br />
Some asked if there was a computable solution. For both the infinite-hats problem and the box-problem if the players have a strategy depending on only a finite number of inputs they can't win. There are ways to measure the complexity of a strategy and it would be interesting to get upper and lower bounds on the complexity of a strategy. And one can look at the following: If the adversary's strategy is of complexity BLAH then what complexity do the players need to beat it?<br />
<br />
Also, in both games AC is used by the players. Eddie Fisher pointed out that if you toss out AC and instead have the AC AM (all sets are measurable) then the Adversary wins the hat game. Not sure about the box game. One can look at what happens in various axiom systems.<br />
<br />
So many open questions, so little time!<br />
<br />
<br />
<br />
<br />
<div>
<br /></div>
<br />http://blog.computationalcomplexity.org/2016/07/solution-to-alice-bob-box-problem.htmlnoreply@blogger.com (GASARCH)10tag:blogger.com,1999:blog-3722233.post-7318863541466872803Thu, 14 Jul 2016 13:04:00 +00002016-07-14T13:22:11.576-04:00Solution to the infinite hat problem/a point/a new problem<a href="http://blog.computationalcomplexity.org/2016/07/an-infinite-hat-problem-and-later-point.html">In my last post</a> I asked the following question (I've shortened it here but its the same really.)<br />
<br />
<i>An infinite number of people, labelled 1,2,3,... have hats on their head, RED or BLUE. They must all shout at the same time a color. They want only a finite number of people to not guess their own hat color correctly. Can they do this?</i><br />
<i><br /></i>
YES they can manage to get all but a finite number of hats wrong. Here is what they do in their strategy meeting:<br />
<br />
1) Define an equivalence class on infinite strings of R's and B's: x==y iff x and y differ on only a finite number of places. It is easy to show that this is an Equiv relation. We think of the string as telling us the hat colors of all the people.<br />
<br />
2) An Equiv Rel induces a partition. Choose, for each part of the partition, a representative. They all know all of the representatives.<br />
<br />
NOW, once the hats are put on here is how each person reacts:<br />
<br />
<i>Gee, I see all of those hats out there! Since I see all but my hat I KNOW which partition the hat coloring is in. I look at the representative of that partition. I guess the hat color that I have in that representative.</i><br />
<i><br /></i>
Note that ALL of the people will use the SAME rep, and that rep differs from reality in only a finite number of hats. Therefore the number of incorrect answers is finite.<br />
<br />
POINT- when I show this to my class they often don't like it. Some of course do not understand it, but even those who do sometimes say <i>that's not practical </i>or <i>the people would need infinite brains! </i>These are both true, but I like it anyway. HOW ABOUT YOU- does the solution satisfy?<br />
<br />
NEW PROBLEM (are any problems really new?) I heard this from Peter Winkler who heard it from Sergui Hart who does not claim to have invented it.<br />
<br />
Alice and Bob play a game (My darling complains that when a math puzzle uses the word <i>game</i> its usually not a fun game. This problem will not be a counterexample.)<br />
<br />
There are an infinite number of boxes labelled 1,2,3,....<br />
<br />
Alice puts into each box a natural number.<br />
<br />
(CLARIFICATION based on a comment- Alice an put any number she wants in any box.<br />
She wants to put 18 in both box 199 and box 3999 she can do that. NO restriction on what<br />
Alice puts in the boxes except that every box has SOME natural number. ALSO- she need not<br />
use all the naturals- if she wants to put a 1 in every box, she can.)<br />
<br />
Bob opens all but a finite number of boxes.<br />
<br />
For one of the boxes Bob does NOT open he guesses what the number in it is.<br />
<br />
They then open that box. If Bob is right, he wins. If not then Alice wins.<br />
<br />
Would you rather be Alice or Bob?<br />
<br />
Feel free to post thoughts in the comments, though if you want to solve it without help you may want to avoid the comments. I'll post the answer next week.<br />
<br />
<br />http://blog.computationalcomplexity.org/2016/07/solution-to-infinite-hat-problema.htmlnoreply@blogger.com (GASARCH)18tag:blogger.com,1999:blog-3722233.post-6486629003642999306Mon, 11 Jul 2016 01:29:00 +00002016-07-12T07:16:07.839-04:00An infinite hat problem and later a point<br />
<br />
<i>Problem</i>: There are an infinite number of people. They are labelled 1,2,3,... (<a href="https://www.youtube.com/watch?v=nW-bFGzNMXw">I am not a number, I am a free man</a>!) There is the Master who I call The Master. The Master will, at the same time, put a hat on each persons head. Some of the hats are RED, some are BLUE. (Clarification added later- everyone can see all the peoples hat colors except their own.)<br />
<br />
The people will then all, at the same time, yell out a hat color. (Clarification added later- NO other form of communicationis allowed.)<br />
<br />
If only a finite number of them get their own hat color wrong they win (not sure what they win, but they win!)<br />
<br />
If an infinite number of them get their own had color wrong, then they lose.<br />
<br />
They can discuss strategy ahead of time; however, The Master overhears all conversation.<br />
<br />
Assume that the people and The Master are experts at this game.<br />
<br />
Who would you bet to win? How much and at what odds?<br />
<br />
I'll post the answer, a meta question about it, and another math question, on Thursday.<br />
<br />
Feel free to post your answer as comments. If you do then please also comment on if you've seen the problem before since I'm curious (1) how well known the problem is, and (2) how hard it is to solve if you haven't seen it.<br />
<br />
If you want to try to solve it yourself, don't look at the comments in case the right solution is there.<br />
<br />
<br />
<br />http://blog.computationalcomplexity.org/2016/07/an-infinite-hat-problem-and-later-point.htmlnoreply@blogger.com (GASARCH)16tag:blogger.com,1999:blog-3722233.post-193902680920835467Tue, 05 Jul 2016 03:37:00 +00002016-07-05T07:28:44.983-04:00Is determining if a poly over a finite field is 1-1 hard? Sure seems so.<br />
When I teach cryptography to High School students I begin with shift and linear ciphers which are<br />
<br />
x --> x+s mod 26 (s is a shift, x is a letter of the alphabet. Hmm- x really IS a letter of the alphabet!)<br />
<br />
x--> ax+b mod 26 (Note that a has to be rel prime to 26.)<br />
<br />
I then ask why nobody seems to have ever used<br />
<br />
x --> ax<sup>2</sup> + bx + c mod 26.<br />
<br />
I then tell them that this is because there is no quick test that will, given (a,b,c), tell if<br />
f(x) = ax<sup>2</sup> + bx + c mod 26 is 1-1 (and hence onto).<br />
<br />
It recently dawned on me that I don't really know that its hard to test.<br />
(ADDED LATER) In fact its not true. Algebra shows that f(x) is NOT 1-1 iff<br />
<br />
a(x+y)+b =0 mod 26<br />
<br />
has a solution. If a is rel prime to 26 then clearly there is a solution (many in fact).<br />
If a is not rel prime to 26 then I suspect this is not hard.<br />
<br />
How hard is the following problem?<br />
<br />
Given a poly f(x) of degree d, and n, is f(x) mod n 1-1?<br />
<br />
We will assume all coefficients are between 0 and n.. We can also assume that c is 0 since f(x) is 1-1 then f(x)-c is 1-1.<br />
The coefficients are given in binary so the length of the input is roughly dlog(n).<br />
<br />
One can of course compute f(0), f(1),...,f(n-1) and see if there are any repeats, but this takes O(n) steps which is exp in the input of length log n.<br />
<br />
I suspect that this is either a well known solved problem (either in P or NPC) or a well known open problem. Any help or references will be more appreciated than usual-- see next paragraph.<br />
<br />
I am the new SIGACT News Open Problems Column editor. In the future I will be soliciting people to write columns for me, but the first one I'll do myself and this might be a good topic- if its open! And if it is open, would be good to know references and what is known.<br />
<br />
<br />http://blog.computationalcomplexity.org/2016/07/is-determining-if-poly-over-finite.htmlnoreply@blogger.com (GASARCH)11tag:blogger.com,1999:blog-3722233.post-3491866800616455832Thu, 30 Jun 2016 12:21:00 +00002016-06-30T08:21:26.739-04:00ExcaliburGoro Hasegawa <a href="http://www.nytimes.com/2016/06/26/world/asia/goro-hasegawa-creator-of-othello-board-game-dies-at-83.html">passed away</a> last week at the age of 83. Hasegawa created and popularized the board game Othello based on an old British game Reversi.<br />
<div>
<br /></div>
<div>
Back in the 80's, a high school friend Chris Eisnaugle and I used to write programs together including the Frogger-like program <a href="http://lance.fortnow.com/ribbit/">Ribbit</a> for the Apple II. We decided to try our hands at board games and aimed at Othello as it seemed simpler to manage than the more popular attempts at computer chess. Our first program played awful but we contacted and had some great discussions with Peter Frey, a Northwestern psychology professor who worked on computer games. Frey pointed us to some great techniques like alpha-beta pruning and table look up for edge positions. Who knew that I would become a Northwestern professor myself later in life (2008-2012).<br />
<br /></div>
<div>
Unlike many games, the number of moves in Othello are limited in the end of the game, so even on the old IBM PC we used, we could play a perfect endgame from 14 moves out. So a simple strategy of maximizing mobility in the early game, controlling the edges and corners in the mid-game and a perfect end game give a pretty strong Othello program. We called our game <a href="http://lance.fortnow.com/othello/">Excalibur</a> after King Arthur's sword and the title of a <a href="http://www.imdb.com/title/tt0082348/">great movie</a> telling his tale. We traveled to Cal State Northridge for the 1986 computer Othello tournament and captured third place, not bad considering the limited hardware we used. I entered a human tournament myself and for a brief time ranked the 35th best Othello player in the US. </div>
<div>
<br /></div>
<div>
In 1989 we tried another computer Othello tournament, this time just calling in and coming in fifth place. One of our games was against the eventual winner by then CMU professor <a href="https://en.wikipedia.org/wiki/Kai-Fu_Lee">Kai-Fu Lee</a>. His program beat us of course but he was still impressed with the play of Excalibur. Kai-Fu Lee would later work for Microsoft then leave to build up Google China, leading to one of the more memorable <a href="http://www.cnet.com/news/microsoft-settles-with-google-over-executive-hire/">lawsuits</a> over a non-compete agreement.</div>
<div>
<br /></div>
<div>
<a href="https://en.wikipedia.org/wiki/Computer_Othello">Computer Othello</a> improved greatly since then and in 1997 Michael Buro's game Logistello easily beat the best human players. Michael Buro worked at the NEC Research Institute and we met when I joined in 1999. We chatted Othello but of course Excalibur was not in the same league as Logistello. Michael Buro later would join University of Alberta, which became the academic center for computer games. </div>
<div>
<br /></div>
<div>
Computer Othello gained popularity because no one could create a Computer Go program that could beat good amateurs. That changed with randomized search and machine learning that led to <a href="http://blog.computationalcomplexity.org/2016/02/go-google-go.html">AlphaGo</a>. </div>
<div>
<br /></div>
<div>
So thank you Goro Hasegawa for creating this simple game that played such an interesting part of my life back in the day. </div>
http://blog.computationalcomplexity.org/2016/06/excalibur.htmlnoreply@blogger.com (Lance Fortnow)0tag:blogger.com,1999:blog-3722233.post-8037830445610090135Mon, 27 Jun 2016 03:05:00 +00002016-06-28T16:15:18.290-04:00There is now a Bounded Discrete Envy Free Cake Cutting Protocol!<i>Lance</i>: Bill, there is a new result on cake cutting that was presented at STOC! Do you want to blog about it?<br />
<br />
<i>Bill:</i> Do snakes have hips! Does a chicken have lips!<br />
<br />
<i>Lance</i>: No to the first one and I don't know to the second one.<br />
<br />
<i>Bill:</i> Yes I'll blog about it! Whats the paper?<br />
<br />
<i>Lance</i>: It's <a href="https://arxiv.org/pdf/1604.03655v5.pdf">this</a> paper by Aziz and Mackenzie.<br />
<br />
<i>Bill</i>: Oh. That's not new. Five people emailed me about it a while back. But yes I will blog about it.<br />
<br />
<i>Cake Cutting</i>: There are n people with different tastes in cake (some like chocolate and some... OH, who doesn't like chocolate? Okay, someone prefers kale which is on the cake.) They want a protocol that divides the cake in a way that is fair. What is fair? There are many definitions but I'll talk about two of them.<br />
<br />
<i>Proportional</i>: Everyone gets 1/n of the cake (in their own opinion- I will omit saying this from now on).<br />
<br />
Proportional sounds fair but consider the following scenario: Alice thinks she got 1/3 but she thinks Bob got 1/2 and Eve got 1/6. Alice i will envy Bob.<br />
<br />
<i>Envy Free</i>: Everyone thinks they have the larges piece (or are tied for it).<br />
<br />
What is a protocol? It is a set of instructions and advice so that if (1) if the players all follow the advice then the end result is fair, and (2) if a player does not follow the advice then that player might get less than his fair share. Hence all players are motivated to follow the advice. We assume that everyone acts in their own self interest and that they are at a diamond cutters convention (perhaps co-located with STOC) so they really can cut cake very finely.<br />
<br />
We will only consider discrete protocols. We won't define this formally.<br />
<br />
<i>Prior Results</i>:<br />
1) There is a protocol for Prop fairness for n people that uses O(n log n) cuts. See <a href="http://www.cs.umd.edu/~gasarch/BLOGPAPERS/prop.pdf">my notes</a><br />
<br />
2) Jeff Edmonds and Kirk Pruhs showed a lower bound of Omega(n log n). See <a href="http://www.eecs.yorku.ca/~jeff/research/kirk/cake.lower/talg.pdf">their paper.</a><br />
<br />
3) There is a protocol for Envy Free fairness for 3 people due to Conway and Selfridge. This was in 1960. This protocol took 5 cuts. (It is in the doc I point to in next item)<br />
<br />
4) In 1995 Brams and Taylor obtained a protocol for envy free fairness for n people. But there is a catch- there is no bound on the number of cuts. For all N there is a way to set four peoples tastes so that the protocol takes more than N cuts. See <a href="http://www.cs.umd.edu/~gasarch/BLOGPAPERS/envyfree.pdf">my notes.</a><br />
<br />
All items to follow are for an envy free protocol for n people.<br />
<br />
5) It was an open question to determine if there is a bounded protocol. Stromquest proved that there can be no bounded protocol if all of the players got a contiguous piece, though this was not the case in the Brams-Taylor protocol. See <a href="https://www.cs.umd.edu/users/gasarch/TOPICS/cake/lbenvyfree.pdf">his paper</a><br />
<br />
At the time I thought there would be no bounded protocol. I found a way to measure unbounded protocols using ordinals and wrote a paper on it: See <a href="https://arxiv.org/abs/1507.08497">my paper.</a><br />
<br />
6) Aziz and MacKenzie showed there was a bounded protocol for 4 people. See <a href="http://arxiv.org/abs/1508.05143">their paper.</a><br />
<br />
7) Aziz and MacKenzie, STOC 2016, showed there was, a protocol that takes at most n<sup>O(n)</sup> cuts. Hence a bounded protocol! See <a href="https://arxiv.org/abs/1604.03655">their paper.</a><br />
<br />
What's next? Either improve the number of cuts or show it can't be done!<br />
<br />
<br />http://blog.computationalcomplexity.org/2016/06/there-is-now-bounded-discrete-envy-free_0.htmlnoreply@blogger.com (GASARCH)1tag:blogger.com,1999:blog-3722233.post-8751777274825666398Thu, 23 Jun 2016 12:44:00 +00002016-06-23T08:44:16.603-04:00STOC 2016<div>
I attended the <a href="http://acm-stoc.org/stoc2016/">2016 STOC Conference</a> earlier this week in Cambridge, Massachusetts. No shortage of awesome results highlighted by László Babai's new quasipolynomial-time graph isomorphism algorithm. Babai didn't have a chance to give more than a glimpse into his algorithm in the 20 minute talk but you did see his joy in discovering the concept of "affected" last September, the key to making the whole algorithm work.<br />
<br />
Babai also received the ACM SIGACT Distinguished Service prize for his work for the community including his open-access journal <a href="http://theoryofcomputing.org/">Theory of Computing</a>.<br />
<br />
You can see and access all the papers from the <a href="http://acm-stoc.org/stoc2016/program.html">program page</a>. Links on that page will give you free access to the papers forever. I'll mention some papers here but you'll have to click over on the program page to access them.<br />
<br />
Troy Lee gave my favorite talk on his paper <i>Separations in Query Complexity Based on Pointer Functions</i> with Andris Ambainis, Kaspars Balodis, Aleksandrs Belovs, Miklos Santha and Juris Smotrovs. He gave a wonderful description of a (contrived) function that gives strong separations between deterministic, randomized and quantum decision tree complexity. Scott Aaronson, Shalev Ben-David and Robin Kothari followed up on that work in <i>Separations in query complexity using cheat sheets. </i><br />
<br />
Let me also mention the best paper winners<br />
<ul>
<li><i>Reed-Muller Codes Achieve Capacity on Erasure Channels </i>by Shrinivas Kudekar, Santhosh Kumar, Marco Mondelli, Henry D. Pfister, Eren Sasoglu and Rudiger Urbanke</li>
<li><i>Explicit Two-Source Extractors and Resilient Functions</i> by Eshan Chattopadhyay and David Zuckerman</li>
<li><i>Graph Isomorphism in Quasipolynomial Time </i>by Laszlo Babai</li>
</ul>
<div>
and the Danny Lewin best student paper awardees</div>
<div>
<ul>
<li><i>A Tight Space Bound for Consensus </i>by Leqi Zhu</li>
<li><i>The 4/3 Additive Spanner Exponent is Tight </i>by Amir Abboud and Greg Bodwin</li>
</ul>
</div>
The conference had 327 registrants, 44% students and 74% from the USA. <a href="http://www.computational-geometry.org/">The Symposium on Computational Geometry</a> was held at Tufts before STOC and they held a <a href="http://acm-stoc.org/stoc2016/workshop.html">joint workshop day</a> in between. There were about 20 registered for both conferences.<br />
<br />
STOC had 92 accepted papers out of 370 submissions. None of the three papers claiming to settle P v NP were accepted.<br />
<br />
STOC 2017 will be held in Montreal June 19-23, the first of a theory festival. There will be multiple day poster sessions, a poster for every papers. Invited talks will included best papers from other theory conference. There will be a mild increase in the number of accepted papers. The hope is to draw a broader and larger group of theorists for this festival.<br />
<br />
The first STOC conference was held in Marina del Rey in 1969. That makes the 2018 conference STOC's 50th which will return to Southern California. The Conference on Computational Complexity will co-locate.<br />
<br />
<a href="http://www.wisdom.weizmann.ac.il/~dinuri/focs16/CFP.html">FOCS 2016</a> will be held October 9-11 in New Brunswick, New Jersey preceded by a <a href="https://www.math.ias.edu/avi60">celebration</a> for the 60th birthday for Avi Wigderson.<br />
<br />
<a href="http://siam.org/meetings/da17/">SODA 2017</a> will be held January 16-19 in Barcelona. Paper registration deadline is July 6.<br />
<br /></div>
<div>
If you weren't at the business meeting, it's worth looking at the slides for the <a href="https://thmatters.files.wordpress.com/2016/06/nsf-cise-stoc16-bus-mtg-1.pptx">NSF</a> and the <a href="https://thmatters.files.wordpress.com/2016/06/catcs-report-stoc-2016.pptx">Committee for the Advancement for Theoretical Computer Science</a>. Of particular note, the CATCS site <a href="https://thmatters.wordpress.com/">Theory Matters</a> has <a href="https://cstheory-jobs.org/">job announcements</a> and <a href="https://thmatters.wordpress.com/funding-opportunities-and-tips/career-examples-proposalscomments/">sample CAREER proposals</a>.</div>
http://blog.computationalcomplexity.org/2016/06/stoc-2016.htmlnoreply@blogger.com (Lance Fortnow)3tag:blogger.com,1999:blog-3722233.post-4792566710287614960Tue, 21 Jun 2016 18:54:00 +00002016-06-25T09:21:32.853-04:00When does n divide a_n? The answer, though you already know it. The Point, though its not as strong as I wanted. Oh well.In my last post <a href="http://blog.computationalcomplexity.org/2016/06/when-does-n-divide-in-this-sequence.html">When does n divide a_n?</a> I gave a sequence:<br />
<br />
a(1)=0<br />
<br />
a(2)=2<br />
<br />
a(3)=3<br />
<br />
for all n ≥ 4 a(n) = a(n-2) + a(n-3)<br />
<br />
and I noted that for 2 ≤ n ≤ 23 it looked like<br />
<br />
n divides a(n) iff n is prime<br />
<br />
and challenged my readers to prove it or disprove it.<br />
<br />
I thought it would be hard to find the first counterexample and hence I would make the point:<br />
<br />
<i>Just because a pattern holds for the first 271440 numbers does not mean that it always holds!</i><br />
<i><br /></i>
However, several readers found that 521<sup>2</sup>=271441 is a counterexample. In fact they found it rather quickly. I thought it would take longer since <a href="http://www.solipsys.co.uk/new/FastPerrinTest.html?ColinsBlog">this blog (also my inspiration)</a> by Colin Wright seemed to indicate that fancy data structures and algorithms tricks are needed. So I emailed Colin about this and it turns out he originally wrote the program many years ago. I quote his email:<br />
<br />
---------------------------<br />
> I posted on Perrin Primes (without calling them that) and people seemed to<br />
> find the counterexample, 561^2, easily.<br />
<br />
Yes. These days the machines are faster, and languages with arbitrary<br />
precision arithmetic are common-place. When I first came across this<br />
problem, if you wanted arithmetic on more than 32 bits you had to write<br />
the arbitrary precision package yourself. This was pre-WWW,<br />
although not pre-internet. Quite.<br />
<br />
> So I wondered why your code needed those optimizations.<br />
<br />
Even now, it's easy to find the first few counter-examples, but it rapidly<br />
gets out-of-hand. The sequence grows exponentially, and very soon you are<br />
dealing with numbers that have thousands of digits. Again, not that bad now,<br />
but impossible when I first did it, and even now, to find anything beyond the<br />
first 20 or 30 counter-examples takes a very long time.<br />
<br />
So ask people how to find the first 1000 counter-examples,<br />
and what they notice about them all.<br />
<div>
-----------------------------------------</div>
<div>
<br /></div>
<div>
back to my post:</div>
<br />
It is known that if n is prime then n divides a(n). (ADDED LATER: see <a href="http://math.stackexchange.com/questions/1280125/a-question-about-the-proof-that-for-prime-p-p-divides-kp-where-k-is-the-pe">here</a> for a proof) The converse is false. Composites n such that n divides a(n) are called <a href="https://en.wikipedia.org/wiki/Perrin_number">Perrin Pseudoprimes</a>. The following questions seem open, interesting, and rather difficult:<br />
<br />
1) Why is the first Perrin Pseudoprime so large?<br />
<br />
2) Are there other simple recurrences b(n) where n divides b(n) iff n is prime LOOKS true for a while?<br />
<br />http://blog.computationalcomplexity.org/2016/06/when-does-n-divide-the-answer-though.htmlnoreply@blogger.com (GASARCH)6tag:blogger.com,1999:blog-3722233.post-4804501150043320086Fri, 17 Jun 2016 15:35:00 +00002016-06-17T11:35:27.469-04:00The Relevance of TCS<i>Avi Wigderson responds to yesterday's <a href="http://blog.computationalcomplexity.org/2016/06/karp-v-wigderson-20-years-later.html">post</a>.</i><br />
<br />
20 years is a long time, and TCS is in a completely different place today than it was then.<br />
I am happy to say that internally its members are far more confident of its importance and independence as a scientific discipline, and externally the recognition of that importance by all sciences (including computer science) has grown tremendously. I have no doubt that both will continue to grow, as will its impact on science and technology.<br />
<br />
Let me address a few aspects of the original post (one can elaborate much more than I do here).<br />
<br />
Young talent: The way we continuously draw exceptional young talent to our core questions is not just a fact to state - it carries important meaning, namely a key sign of our health and prosperity. After all, these exceptionally talented young people could have done well in any field in science and technology, and they freely chose us (and indeed have been responsible for the many great results of the field in the past 20 years)!<br />
<br />
Funding levels: In contrast, funding levels are always controlled by few and are subject to political pressures. So here our field was wise to grow up politically and realize the importance of advocacy and PR besides just doing great research. This has definitely helped, as did other factors.<br />
<br />
Growth of theory in academia: I have no idea of the exact statistics (or even how to measure it exactly) but I should note as an anecdote that as soon as Harvard got 12 new positions in CS it made three senior offers to theorists: Cynthia, Madhu and Boaz! I see it as an important critical development to have TCS well represented not only in the top 20 universities but in the top 100. Our educational mission is too important to be reserved only to the elite schools. (Needless to say, our science and way of thinking should be integrated to the K-12 educational system as well. While this is budding, significant meaningful presence will probably take decades.)<br />
<br />
Scientific relevance: While it may be too early to evaluate the true impact of our (many) specific incursions into and collaborations with Biology, Economics, Physics, Mathematics, Social Science etc., I believe the following general statement. *The emerging centrality of the notion of algorithm, and the limits of its efficient utilization of relevant resources, is nothing short than a scientific revolution in the making.* We are playing a major role in that revolution. Some of the modeling and analysis techniques we have developed and continue to develop, and even more, the language we have created over the past half century to discuss, invent and understand processes, is the fuel and catalyst of this revolution. Eventually all scientists will speak this language, and the algorithmic way of thought will be an essential part of their upbringing and research.<br />
<br />
Technological relevance: Even without going to great past achievements which are taken for granted and dominate technological products, and considering only current TCS work evidence is staggering. Sublinear algorithms, Linear solvers, Crypto (NC0-crypto, Homomorphic encryption,...), Privacy, Delegation, Distributed protocols, Network design, Verification tools, Quantum algorithms and error correction, and yes, machine learning and optimization as well, are constantly feeding technological progress. How much of it? Beyond counting patents, or direct implementations of conference papers, one should look at the integration of modeling and analysis techniques, ways of thinking, and the sheer impact of "proofs of concept" that may lead to drastically different implementations of that concept. Our part in the education we provide to future developers was, is and should be of central influence on technology.<br />
<br />
In a tiny field like ours, having the impact we do on so many scientific and technological fields that are factors 10-100 larger than us may seem miraculous. Of course we know the main reason since Turing - we have universality on our side - algorithms are everywhere. What is perhaps more miraculous is the talent and willingness of pioneers in our field over decades to search, interact, learn and uncover the numerous forms of this universal need in diverse scientific and technological fields, and then suggest and study models using our language and tools. This has greatly enriched not only our connections and impact on other disciplines, but also had the same effect on our intrinsic challenges and mysteries, many of which remain widely open. I am happy to say that at least part of that remarkable young talent constantly drawn into our field keeps focus on these intrinsic challenges and the natural, purely intellectual pursuits they lead to. Our history proves that there are direct connections between the study and progress on core questions and our interactions with the outside world. Our current culture luckily embraces both!<br />
<br />
All the above does not mean that we can't improve on various aspects, and constant questioning and discussion are welcome and fruitful. But I believe that a the firm foundation of these deliberations should be the intrinsic scientific importance of our mission, to understand the power, limits and properties of algorithms of all incarnations, shapes and forms, and the study of natural processes and intellectual concepts from this viewpoint. This importance does not depend on utility to other disciplines (it rather explains it), and should not seek justification from them. The correct analogy in my view is expecting theoretical physicists to seek similar confirmation in their quest to uncover the secrets of the universe.http://blog.computationalcomplexity.org/2016/06/the-relevance-of-tcs.htmlnoreply@blogger.com (Lance Fortnow)14tag:blogger.com,1999:blog-3722233.post-1733567208294013592Thu, 16 Jun 2016 12:19:00 +00002016-06-16T08:19:13.887-04:00Karp v Wigderson 20 Years LaterThe <a href="http://acm-stoc.org/stoc2016/">48th ACM Symposium on the Theory of Computing</a> starts this weekend in Boston. Let's go back twenty years to the 28th STOC, part of the second Federated Computing Research Conference in Philadelphia. A year earlier in June of 1995, the NSF sponsored a workshop with the purpose of assess the current goals and directions of the theory community. Based on that workshop a committee, chaired by Richard Karp, presented their report <a href="https://www.dropbox.com/s/4ipc142gsl5571b/karp-report.pdf?dl=0">Theory of Computing: Goals and Directions</a> at the 1996 STOC conference. While the report emphasized the importance of core research, the central thesis stated<br />
<blockquote class="tr_bq">
In order for TOC to prosper in the coming years, it is essential to strengthen our communication with the rest of computer science and with other disciplines, and to increase our impact on key application areas.</blockquote>
Oded Goldreich and Avi Wigderson put together a competing report, <a href="https://www.dropbox.com/s/aox8ga8uzmbjesx/toc-sp1.pdf?dl=0">Theory of Computing: A Scientific Perspective</a> that focuses on theory as a scientific discipline.<br />
<blockquote class="tr_bq">
In order for TOC to prosper in the coming years, it is essential that Theoretical Computer Scientists concentrate their research efforts in Theory of Computing and that they enjoy the freedom to do so. </blockquote>
There was a lively discussion at the business meeting, with Karp and Christos Papadimitriou on one side, with Goldreich and Wigderson on the other. I remember one exchange where one side said that the people who implement an algorithm should get as much credit as those who developed it. Avi, I believe, said he'd like to see the implementer go first.<br />
<br />
So what has transpired in the last two decades. The theory and community has not withered and died, the field continues to produce great results and attract many a strong student. On the other hand the theory community has not had the growth we've seen in other CS areas, particularly in the recent university expansion. Industrial research in core theory, which had its highs in the 90's, has dwindled to a small number of researchers in a few companies. Foundation research has helped some, IAS now has a faculty position in theoretical CS, the Simons Foundation funds some faculty and recently started an institute in Berkeley and the Clay Mathematics Institute has given the field a considerate boost by naming the P v NP problem as one of their millennial challenges.<br />
<br />
The main core theory conferences, STOC, FOCS, SODA, Complexity and others have continued to focus on theorems and proofs. Rarely do the research in these papers affect real-world computing. The theory community has not played a major role in the growth of machine learning and has left real-world optimization to the operations research community.<br />
<br />
We have seen some other developments making some progress in connecting theory to applications.<br />
<ul>
<li>1996 saw the first <a href="https://en.wikipedia.org/wiki/Paris_Kanellakis_Award">Kanellakis Prize</a> to honor "specific theoretical accomplishments that have had a significant and demonstrable effect on the practice of computing"</li>
<li>Some companies, most notably Akamai, have come out of the theory community and helped shape real-world computing.</li>
<li>We have seen new research communities in EC and Quantum Computing that connect with economists and physicists. </li>
<li>The NSF now has a program <a href="http://www.nsf.gov/pubs/2016/nsf16515/nsf16515.htm">Algorithms in the Field</a> that connects theorists with applied computer scientists.</li>
<li>Some theory topics like differential privacy have entered the mainstream discussion.</li>
</ul>
<div>
We live in a golden age of computer science and computing research is transforming society as we know it. Do we view ourselves as a scientific discipline divorced from these changes, or should theory play a major role? This is a discussion and debate the theory community should continue to have. </div>
http://blog.computationalcomplexity.org/2016/06/karp-v-wigderson-20-years-later.htmlnoreply@blogger.com (Lance Fortnow)16tag:blogger.com,1999:blog-3722233.post-6704204702231101478Mon, 13 Jun 2016 02:56:00 +00002016-06-12T22:56:51.208-04:00When does n divide a_n in this sequence?Consider the following sequence:<br />
<br />
a(1)=0<br />
<br />
a(2)=2<br />
<br />
a(3)=3<br />
<br />
for all n ≥ 4 a(n) = a(n-2)+a(n-3)<br />
<br />
Here is a table of a(n) for 2 ≤ n ≤ 23<br />
<br />
n 2 3 4 5 6 7 8 9 10 11 12<br />
a(n) 2 3 2 5 5 7 10 12 17 22 29<br />
<br />
n 13 14 15 16 17 18 19 20 21 22 23<br />
a(n) 39 51 68 90 119 158 209 277 367 486 644<br />
<br />
For 2≤ n ≤ 23 the n such that n divides a(n) are<br />
<br />
n = 2,3,5,7,11,13,17,19,23.<br />
<br />
Notice a pattern? Of course you do!<br />
<br />
I propose the following question which I will answer in my next post (in a week or so)<br />
<br />
PROVE or DISPROVE the following:<br />
<br />
for all n≥ 2 n divides a(n) iff n is prime.<br />
<br />
<br />
<div>
<br /></div>
http://blog.computationalcomplexity.org/2016/06/when-does-n-divide-in-this-sequence.htmlnoreply@blogger.com (GASARCH)14tag:blogger.com,1999:blog-3722233.post-8565965427617437841Thu, 09 Jun 2016 12:51:00 +00002016-06-09T08:51:59.000-04:00Math MoviesIn 1997 <a href="http://www.imdb.com/title/tt0119217/">Good Will Hunting</a>, a fictional movie about the hidden mathematical talents of a MIT janitor grossed $225 million and won a best screenplay Oscar for Matt Damon and Ben Affleck. At the time the chair of the Chicago math department told me how much he disliked the movie given the way mathematics and mathematicians were portrayed. I told him the movie made math seem exciting and brought public awareness of the Fields medal, mentioned several times in the movie. You can't buy that kind of publicity for an academic field.<br />
<br />
In 2001 <a href="http://www.imdb.com/title/tt0268978/">A Beautiful Mind</a>, on the life of John Nash grossed $313 million in the box office and won the best picture Oscar. In 2014 we saw critically acclaimed movies <a href="http://www.imdb.com/title/tt2084970">The Imitation Game</a> (8 Oscar nominations with a win for adapted screenplay and $233 million gross) on Alan Turing and <a href="http://www.imdb.com/title/tt2980516/">The Theory of Everything</a> (5 nominations with a win for best actor, $123 million) on Stephen Hawking. These movies focused more on the struggles of the lead character than the science itself. Though these movies had their flaws they did show to a popular audience that the goal of math and science are worth an incredible struggle.<br />
<br />
And complain all you want about the 2005 TV series <a href="https://en.wikipedia.org/wiki/Numbers_(TV_series)">Numbers</a>, but get your head around the fact that a show about a crime-solving mathematician lasted six seasons. <a href="https://en.wikipedia.org/wiki/The_Big_Bang_Theory">The Big Bang Theory</a> remains the top US television comedy heading into its tenth season this fall.<br />
<br />
Which takes us to the recent movie <a href="http://www.imdb.com/title/tt0787524/">The Man Who Knew Infinity</a> about the life of Ramanujan, a movie that has gotten <a href="http://www.math.columbia.edu/~woit/wordpress/?p=8427">wide</a> <a href="http://www.scottaaronson.com/blog/?p=2707">excitement</a> <a href="http://blogs.ams.org/mathgradblog/2016/05/02/man-knew-infinity-mathematical-movie">from</a> <a href="http://blogs.ams.org/blogonmathblogs/2016/05/27/the-ramanujan-movie">mathematicians</a> for the portrayal of the math itself, with credit given to consulting mathematician Ken Ono. I haven't seen the movie as it has barely played in Atlanta. It got critically mixed reviews, grossed only $3.4 million and will probably be forgotten in award season. The Ramanujan story is just not that dramatically interesting.<br />
<br />
What's more important: Getting the math right, or taking some liberties, telling a good story and drawing a large audience. Can you actually do both? Because you can't inspire people with a movie they don't see.http://blog.computationalcomplexity.org/2016/06/math-movies.htmlnoreply@blogger.com (Lance Fortnow)5tag:blogger.com,1999:blog-3722233.post-3319929913349181061Mon, 06 Jun 2016 02:33:00 +00002016-06-06T17:45:59.226-04:00What do Evolution, Same Sex Marriage, and Abstract Set Theory have in Common?(This post is based on articles from 2012 so it may no longer be true. Also- to be fair- I tried finding stuff on the web BY the people who object to our children being exposed to abstract set theory but could not, so this article is based on hearsay.)<br />
<div>
<br /></div>
<div>
Louisiana has a voucher system for poor kids to go to other schools, including religious ones. I am not here to debate the merits of that or the state of US education. However, from <a href="http://m.motherjones.com/blue-marble/2012/07/photos-evangelical-curricula-louisiana-tax-dollars">this article</a> it seems that they are learning some odd things.</div>
<div>
<br /></div>
<div>
As you would expect, some Christian schools teach that Evolution did not occur, same sex marriage is wrong (actually their opinion of gay people is far more negative than just being against same sex marriage), and that Abstract Set theory is evil.(Note- Catholic Schools have no problem with Evolution, in fact, the catholic church has never had a problem with it.)<br />
<br />
Come again? Yes we would expect these opinions on evolution and same sex marraige, but Abstract Set Theory? Why? Its explained in <a href="http://boingboing.net/2012/08/07/what-do-christian-fundamentali.html">this article</a> but I'll say briefly that they don't like the post-modern view of mathematics where anything goes. The coherent version of their point of view is that they are Platonists. A less charitable view is that they find Abstract Set Theory too dang hard. I've also seen somewhere that they object to Cantor's theory since there is only one infinity and it is God.<br />
<br />
The book <a href="http://www.amazon.com/Infinitesimal-Dangerous-Mathematical-Theory-Shaped/dp/0374534993">Infinitesimals: How a dangerous mathematical theory shaped the modern world</a> is about an earlier time, around 1600, when the Catholic church thought that using infinitesimals was... bad? sinful? contrary to the the laws of God and Man? (I reviewed it <a href="https://www.cs.umd.edu/users/gasarch/BLOGPAPERS/inf.pdf">here</a>) I though we were no longer living in a time where religion had an influence on Mathematics. And, to be fair, we ARE past that time. But this voucher program worries me. And I haven't even got to what they do to American History.<br />
<br />
<br />
<br />
<br /></div>
http://blog.computationalcomplexity.org/2016/06/what-do-evolution-same-sex-marriage-and.htmlnoreply@blogger.com (GASARCH)16tag:blogger.com,1999:blog-3722233.post-5799462906974107688Thu, 02 Jun 2016 14:07:00 +00002016-06-02T10:07:50.264-04:00CCC 2016Earlier this week I attended the <a href="http://www.al.ics.saitama-u.ac.jp/elc/ccc/">31st Computational Complexity Conference</a> in Tokyo. I've been to thirty of these meetings, missing only the 2012 conference in Porto. Eric Allender has attended them all.<br />
<br />
The conference had a 130 participants with fewer women than you can count on one hand and 26 made it from the States. There were 34 accepted papers out of 91 submitted.<br />
<br />
The <a href="http://drops.dagstuhl.de/portals/extern/index.php?semnr=16003">proceedings</a> are fully open access though the Dagstuhl LIPICS series, including the <a href="http://dx.doi.org/10.4230/LIPIcs.CCC.2016.19">paper</a> by Rahul Santhanam and myself that I presented at the meeting. The <a href="http://dx.doi.org/10.4230/LIPIcs.CCC.2016.10">best paper</a> by Marco Carmosino, Russell Impagliazzo, Valentine Kabanets and Antonina Kolokolova drew a surprising strong connection between natural proofs and learning theory. In one of my favorite other talks, John Kim and Swastik Kopparty show <a href="http://dx.doi.org/10.4230/LIPIcs.CCC.2016.11">how to decode Reed-Muller codes</a> over an arbitrary product set instead of a structured field.<br />
<br />
The German government will in the future no longer support LIPICS due to EU rules to prevent unfair competition with the commercial publishers. (Don't shoot the messenger) LIPICS will continue, the conferences will have to spend a little more to use them.<br />
<br />
Next year's conference will be in Riga, Latvia July 6-9 right before ICALP in Warsaw. The 2018 meeting is likely to take place closely located to STOC in southern California.<br />
<br />
Osamu Watanabe put together this <a href="https://youtu.be/3SzEHkk0Fmk">slide show</a> for the conference reception featuring pictures of attendees of the Complexity Conference through the ages, including the authors of this blog.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<iframe allowfullscreen="" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/s_vi/3SzEHkk0Fmk/default.jpg?sqp=CLTbuLoF&rs=AOn4CLAPnQXCqKrbA8dvOxz-pdlwP0mjxQ" frameborder="0" height="266" src="https://www.youtube.com/embed/3SzEHkk0Fmk?feature=player_embedded" width="320"></iframe></div>
<br />
Peter van Emde Boas forwarded the <a href="https://www.dropbox.com/s/rij1f2odazjisuz/callstruct1_1985_838.pdf?dl=0">call for papers</a> and <a href="https://www.dropbox.com/s/b0dhvwgxtwvxvmb/orgstruct1_1985_839.pdf?dl=0">initial letters</a> for the very first conference, originally called Structure in Complexity Theory.http://blog.computationalcomplexity.org/2016/06/ccc-2016.htmlnoreply@blogger.com (Lance Fortnow)1tag:blogger.com,1999:blog-3722233.post-7077840493326820837Mon, 30 May 2016 04:20:00 +00002016-06-05T02:01:04.169-04:00New Ramsey Result that will be hard to verify but Ronald Graham thinks its right which is good enough for me.<br />
If you finitely color the natural numbers there will be a monochromatic solution to<br />
<br />
x+2y+3z - 5w = 0<br />
<br />
There is a finite coloring of the natural numbers such that there is NO monochromatic solution to<br />
<br />
x+2y+3z - 7w = 0<br />
<br />
More generally:<br />
<br />
An equation is REGULAR if any finite coloring of the naturals yields a mono solution.<br />
<br />
RADO's THEOREM: A linear equation a1 x1 + ... + an xn = 0 is regular IFF some subset of the ai's sums to 0 (the ai's are all integers).<br />
<br />
Rado's theorem is well known.<br />
<br />
What about other equations? Ronald Graham has offered $100 to prove the following:<br />
<br />
For all two colorings of the naturals there is a mono x,y,z such that<br />
<br />
x<sup>2</sup> + y<sup>2</sup> = z<sup>2 </sup><br />
<br />
I've seen this conjecture before and I thought (as I am sure did others) that first there would be a prove that gave an ENORMOUS bound on<br />
<br />
f(c) = the least n such that for all c-colorings of {1,...,n} there is a mono (x,y,z) such that ...<br />
<br />
and then there would be some efforts using SAT solvers and such to get better bounds on f(c).<br />
<br />
This is NOT what has happened. Instead there is now a <a href="http://arxiv.org/abs/1605.00723">paper</a> by Heule, Kullmann, Marek, where they show f(2)=7825.<br />
<br />
(NOTE- ORIGINAL POST HAD f(2)-7285. Typo, was pointed out in one of the comments<br />
below. Now fixed.)<br />
<br />
<br />
It is a computer proof and is the longest math proof ever. They also have a program that checked that the proof was correct.<br />
<br />
And what did they get for their efforts? A check from Ronald Graham for $100.00 and a blog entry about it!<br />
<br />
While I am sure there proof is correct I wish there was a human-readable proof that f(2) existsed even if it gave worse bounds. For that matter I wish there was a proof tha,t for all c, f(c) exists. Maybe one day; however, I suspect that we are not ready for such problems.<br />
<br />
<br />
<sup><br /></sup>
<sup><br /></sup>
<br />
<br />
<br />
<br />http://blog.computationalcomplexity.org/2016/05/new-ramsey-result-that-will-be-hard-to.htmlnoreply@blogger.com (GASARCH)7