tag:blogger.com,1999:blog-37222332017-07-28T08:52:20.828-04:00Computational ComplexityComputational Complexity and other fun stuff in math and computer science from Lance Fortnow and Bill GasarchLance Fortnowhttps://plus.google.com/101693130490639305932noreply@blogger.comBlogger2502125tag:blogger.com,1999:blog-3722233.post-71436131507024627122017-07-28T08:52:00.000-04:002017-07-28T08:52:20.836-04:00Peter Wegner (1932-2017)<div class="separator" style="clear: both; text-align: center;">
<a href="https://cs.brown.edu/media/uploads/zinnia/2017/07/27/wegnerjpg300x300_q85.jpg.300x300_q85.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="300" data-original-width="200" height="200" src="https://cs.brown.edu/media/uploads/zinnia/2017/07/27/wegnerjpg300x300_q85.jpg.300x300_q85.jpg" width="132" /></a></div>
Peter Wegner <a href="https://cs.brown.edu/news/2017/07/27/memoriam-peter-wegner-1932-2017/">passed away</a> yesterday morning at the age of 84. As a child he <a href="http://posts.cs.brown.edu/2016/05/31/peter-wegner-life-remarkable/">escaped Stalinist Russia and Nazi-occupied Austria</a> the latter via the Kindertransport to England. Wegner would go on to be an important computer scientist at Brown working on CS research and education.<br />
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With Dina Goldin, Peter Wegner developed a notion of <a href="https://doi.org/10.1007/s11023-007-9083-1">interactive computation</a> and used it to argue for the incompleteness of the Church-Turing thesis. While I <a href="http://blog.computationalcomplexity.org/2006/07/principles-of-problem-solving-tcs.html">didn't agree</a> with this interpretation, I appreciated Wegner's efforts to understanding the basic nature of computing. Peter Wegner later organized an ACM Ubiquity Symposium <a href="http://ubiquity.acm.org/symposia2011.cfm?volume=2011">What is Computation?</a> where he sought many view on the question, including <a href="http://ubiquity.acm.org/article.cfm?id=1921573">my own</a>.<br />
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Peter Wegner said "In computer science we work with possibilities and hope we’ll someday be able to solve them." Here's to all things possible.<br />
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<br />Lance Fortnowhttps://plus.google.com/101693130490639305932noreply@blogger.com0tag:blogger.com,1999:blog-3722233.post-48679289600854059832017-07-27T07:42:00.001-04:002017-07-27T07:42:28.522-04:00Lessons from NorwayFor the last two weeks, the wife and I took a vacation to beautiful Norway to see the fjords and the North Cape, effectively the northernmost point in Europe. It was a visit though to the <a href="http://www.norskolje.museum.no/en/">Norwegian Petroleum Museum</a> in Stavanger that inspired this post.<br />
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The discovery of oil in the waters off Norway in 1969 completely changed the Norwegian economy, changing the way of life from a difficult agriculture and fishing society to a more comfortable oil-based economy. The museum had a surprisingly good introductory movie "Oil Kid" describes the challenging relationship of a man with his father who drew a comfortable life as an oil worker. Oil may have made Norway complacent as it lags behind its Scandinavian neighbors in non-oil based <a href="https://techcrunch.com/2016/06/26/after-oil-norway-looks-to-startups-for-economic-growth/">technological innovation</a>.<br />
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The Norwegian government declared that the oil belonged to the people and created a fund that now totals nearly a trillion US dollars, over $150,000 per Norwegian citizen. Nevertheless as the price of oil remains low, Norway risks challenges as a country reliant on its production.</div>
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Norway now aims to be energy-neutral in the near future with extensive hydropower and wind mills. Norway has the highest percentage of electric cars of any country. The tiny town of Eidfjord, population about 1000, has a Tesla charging station. Odd to see this from a major oil exporter.</div>
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As computer scientists we have "struck oil," also leading a revolutionary change to our economy with its winners and losers. In fifty years will we look back and regret what we have wrought? </div>
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Lance Fortnowhttps://plus.google.com/101693130490639305932noreply@blogger.com0tag:blogger.com,1999:blog-3722233.post-81736208597344399942017-07-23T14:39:00.001-04:002017-07-23T14:39:46.532-04:00What are the top Computer science programs for women?What are the top Computer Science Programs for Women?<br />
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How would one even answer the question?<br />
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Some people did a study based on National Center for Education Statistics and Payscale. The results are <a href="https://studysoup.com/blog/education-2/top-computer-science-programs-for-women/">here</a>.<span id="goog_1120995172"></span><br />
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1) While I believe the top X school listed are pretty good for women in computing I don't believe that (say) the Yth school is better than the (Y+1)th school for some values of X and all values of Y.<br />
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2) I appreciate that they put in the work for this.<br />
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3) Overall good news and bad news:<br />
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The number of female professionals in computer science has fallen by 35% since 1990<br />
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The number of women finishing a comp sci degree has increased by 75% in the last five years.<br />
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4) Why do we care? If there are many talented people in group X who are being discouraged from going into field Y, but society needs more people in field Y then YES we should do something about that. Also, if a certain group of people is shut out then a group-think might occur.<br />
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5) What to do? Organizations like <a href="https://girlswhocode.com/">Girls who code</a> are good. The younger they start the bettter.<br />
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6) Is there a social stigma for women to go into computer science? I think the answer is yes. How can we break that stigma? Realize that the notion of a female lawyer or doctor at one time had a stigma but I don't think it does anymore. What did they do right? What are we doing wrong?<br />
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7) Personal note:<br />
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I have mentored 58 High School Students. 56 were male, 2 were female.<br />
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I have mentored 45 ugrad students. 33 were male, 12 were female.<br />
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I have supervised 17 Masters students. 15 were male, 2 were female<br />
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I have supervised 7 PhD students, 6 were male, 1 was female.<br />
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The HS students stats are the most startling (at least to me). I don't have much control on this one as HS students seek me out and they happen to mostly be male. Reading that over it sounds weak on my part.<br />
<br />GASARCHhttp://www.blogger.com/profile/06134382469361359081noreply@blogger.com16tag:blogger.com,1999:blog-3722233.post-65924976900123235812017-07-20T17:47:00.002-04:002017-07-21T08:55:54.672-04:00I would call these Galois Games but I can'tHere is a game (Darling says I only blog about non-fun games. This post will NOT prove her wrong.)<br />
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Let D be a domain, d ≥ 1 and 0 ≠ a<sub>0</sub> ∈ D. There are two players Wanda (for Wants root) and Nora (for No root). One of the players is Player I, the other Player II.<br />
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(1) Player I and II alternate (with Player I going first) choosing the coefficients in D of a polynomial of degree d with the constant term preset to a<sub>0</sub>.<br />
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(2) When they are done, if there is a root in D then Wanda wins, else Nora wins.<br />
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There is a paper by Gasarch-Washington-Zbarsky <a href="https://arxiv.org/abs/1707.04793">here</a> where we determine who wins the game when D is Z,Q (these proofs are elementary), any finite extension of Q (this proof uses hard number theory), R, C (actually any algebraic closed field), and any finite field.<br />
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How did I think of this game? There was a paper called <a href="https://arxiv.org/abs/1110.1137">Greedy Galois Games</a> (which I blogged about <a href="http://blog.computationalcomplexity.org/2013/08/what-are-galois-games.html">here</a>). When I saw the title I thought the game might be that players pick coefficients from Q and if the final polynomial has a solution in radicals then (say) Player I wins. That was not correct. They only use that Galois was a bad duelist. Even so, the paper INSPIRED me! Hence the paper above! The motivating problem is still open:<br />
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<b>Open Question:</b> Let d be at least 5. Play the above game except that (1) the coefficients are out of Q, and (2) Wanda wins if the final poly is solvable by radicals, otherwise Nora wins. (Note that if d=1,2,3,4 then Wanda wins.) Who wins?<br />
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If they had named their game Hamilton Game (since Alexander Hamilton lost a duel) I might have been inspired to come up with a game about quaternions or Hamiltonian cycles.<br />
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POINT- take ideas for problems from any source, even an incorrect guess about a paper!<br />
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<br />GASARCHhttp://www.blogger.com/profile/06134382469361359081noreply@blogger.com2tag:blogger.com,1999:blog-3722233.post-34147018865102306032017-07-17T09:26:00.002-04:002017-07-18T11:29:16.752-04:0089944 Hat Problems<br />
I've blogged about different hat problems a few times (see <a href="http://blog.computationalcomplexity.org/search?q=hats">here</a>). The question arises: How many hat problems are there? The answer is really infinite (literally) but I will list some parameters and bound them reasonably to get an upper bound. Some of the combinations don't make sense, but we'll live with that. (I am also working on a website of hat problem papers. Its nowhere near finished yet and maybe never will be, but its <a href="https://www.cs.umd.edu/users/gasarch/TOPICS/hats/hats.html">here</a> for your benefit. And for mine-- if there are some obvious papers I've omitted then comment or email me.)<br />
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First off, what is a hat problem? Ignoring many parameters: There are n people and c different colors of hats and they are put on people's heads and the people have to guess what color hat they have on. They can see some or all of the other people. I'll mention one that has someone's name on it:<br />
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Winkler's Hat Problem (Peter Winkler proposed it <a href="http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=F55E6F6A731D0AFD04FC39F81BDF7C8A?doi=10.1.1.102.8855&rep=rep1&type=pdf">here</a> along with some other hat problems and some non-hat problems that are also fun)<br />
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<i>There are n people and 2 color hats. An adversary will put the hats no peoples heads. The people must guess simultaneously their hat color. Maximize how many get it right in the worst case.</i><br />
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<i>(ADDED LATER: While I have seen the above referred to as Winkler's Hat Problem, Winkler</i><br />
<i>himself told me that hs problem has the hats put on RANDOMLY, not by an adversary.)</i><br />
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</i> Peter Winkler and later a paper by Ebert et al. (Not Ebert of Siskel and Ebert--- to bad, that would be awesome!) that I mention below seem to have popularized hat games somewhat. But this post is not about their history its about<br />
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<i>how many hat games are there?</i><br />
<i><br />
</i> Here are some parameters I've seen for hat games. If you know of any others please comment!<br />
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1) Is the number of hats finite, infinite (and assume AC), infinite (but don't assume AC). I could say that since there are infinitely many infinities this is an infinite number of parameters, but we'll stick to countable and say this is a 3-valued parameter. A paper on infinite number of hats is <a href="https://www.cs.umd.edu/users/gasarch/TOPICS/hats/infinite-hats-and-ac.pdf">here</a>.<br />
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2) The two most common puzzles are to have the people either all see each other, or in a line where person i sees person j iff i ≤ j. This can be viewed as the people are on K<sub>n</sub> or L<sub>n</sub>. There have been some papers on cycles (see <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v24i1p37/pdf">here</a>, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v24i1p45/pdf">here</a>), triangle-free graphs (see <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v23i1p48/pdf">here</a>), some directed graphs (see <a href="https://www.blogger.com/%C2%A0%C2%A0http://www.combinatorics.org/ojs/index.php/eljc/article/view/v19i1p30/pdf">here</a>), a PhD that studies the problem on cycles (see <a href="https://www.cs.umd.edu/users/gasarch/TOPICS/hats/graphsphd.pdf">here</a>), and a paper with several graphs (see <a href="https://www.blogger.com/%C2%A0https://www.cs.cornell.edu/~rdk/papers/Hats.pdf">here</a>). Formally this would be an infinite-valued parameter, but we'll take the number of classes of graphs that actually have been studied to be 4.<br />
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3) Do the people all guess their hat at the same time OR is there some ordering OR in rounds 3-valued.<br />
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4) Are people allowed to pass or not? (if they are then usually we demand that at least one does not pass). 2-valued. The paper by Ebert-Merkle-Vollmer which allowed passing got a lot of attention and brought hat problems to the general public. Its <a href="http://www.math.uni-heidelberg.de/logic/merkle/ps/SICOMP-autored.pdf">here</a>. A generalization of Ebert's version is <a href="http://theory.stanford.edu/~yuhch123/files/HatGuessing.pdf">here</a>. Ebert's game but on a line is studied <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v17i1r86/pdf">here</a><br />
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5) Are the hats put on by an adversary who can hear your strategy (I've never seen a paper about an adversary who can't hear your strategy) or uniformly randomly or random with some known probability. The last case has been studied in several papers by Theo van Uem (see <a href="https://arxiv.org/pdf/1612.00276.pdf">here</a>, <a href="https://arxiv.org/ftp/arxiv/papers/1704/1704.04244.pdf">here</a>, <a href="https://arxiv.org/ftp/arxiv/papers/1612/1612.05924.pdf">here</a>). 3 valued<br />
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6) The players strategy can be deterministic or randomized. 2-valued. Butler et. al's paper about deterministic strategies covers a lot of material: <a href="https://www.cs.cornell.edu/~rdk/papers/Hats.pdf">here</a>. 2 valued.<br />
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7) What is the goal? To get as many right as possible all the time? To get the expected number right as large as possible (prob may be based on either the random placement of hats or the random strategy of the players). There are even more variations here such as you want for each color there is a guaranteed fraction that get it right (see <a href="http://madhu.seas.harvard.edu/papers/2005/auction-full.pdf">here</a>) 3-valued<br />
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8) Is there some other information available. Examples I've seen: (a) at least one hat is RED, (b) for each color there is a bound on how many hats there are of that color, (c) the hats are natural numbes x,y, and x+y. (see <a href="https://arxiv.org/pdf/0710.2685.pdf">here</a>) (d) there are n+1 colors, n people, and each perosn has a different color (see <a href="http://www.tanyakhovanova.com/publications/ALineOfWizards.pdf">here</a>). Many values depending on the information given, but we'll just say 4-valued, the info above and no info.<br />
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9) Can some other information be revealed first? I've seen a paper where first everyone who sees a RED hat raises their hand. 2-valued.<br />
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10) Is a delay allowed? There are some puzzles where the people do reasoning about what others might deduce, so there is a delay in answers. 2-valued<br />
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11) I've never seen this- but how about trying to make sure that everyone gets it WRONG. 2-valued<br />
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12) I don't count this as a hat problem but some do: they want to find collectively information about all of the hats. Aspnes et al has 0-1 valued hats and wants to simul vote on the parity, see <a href="http://www.cs.yale.edu/homes/aspnes/papers/stoc91voting.pdf">here</a>. 2-valued.<br />
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This puts an upper bound on the number of possible hat puzzles at<br />
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3 x 4 x 3 x 2 x 3 x 2 x 3 x 4 x 2 x 2 x 2 x 2 = 89944.<br />
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This figure is wrong for reasons for reasons that both argue higher and lower.<br />
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a) Lower: MANY of these combinations do not work together. For example, if you have an adversary and a deterministic strategy you can't talk about doing well in the average case.<br />
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b) Higher: For many of the above categories my number-of-values is low. For example you could look at hat games on many different graphs.<br />
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c) Higher: there are other variants I have not listed. That's where YOU come in! If you know of a version I have not discussed then please comment or email it to me!<br />
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<br />GASARCHhttp://www.blogger.com/profile/06134382469361359081noreply@blogger.com5tag:blogger.com,1999:blog-3722233.post-43964326250441961862017-07-13T15:50:00.004-04:002017-07-13T15:50:51.581-04:00Solutions to some Hat Problem AND some points of interest.In my last blog <a href="http://blog.computationalcomplexity.org/2017/07/two-hat-problems-you-may-or-may-not.html">here</a> I asked three (known) hat problems since they may be new to you (one of them I just learned last week) and I had a point to make about them. I have WRITTEN UP the proofs <a href="https://www.cs.umd.edu/users/gasarch/BLOGPAPERS/hats.pdf">here</a> since html is clumsy with math (or I'm clumsy with html-math), so this post is mostly about the points to make about these problems. I would urge you to read the writeup pointed to before reading the post.<br />
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1) N people 1,...,N, two colors R,B, Hats put on RANDOMLY (no adversary).<br />
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People are in a line and pe sees person j's hat iff i ≤ j .<br />
<n ...="" .="" 1="" 2="" and="" at="" attempt="" color="" does="" everyone="" gets="" hat="" in="" least="" maximize="" n.="" not="" one="" or="" order:="" p="" pass.="" pass="" person="" prob="" right="" say="" that="" the="" their="" then="" they="" to="" want="" we="" who="" will=""><br /></n>
<n ...="" .="" 1="" 2="" and="" at="" attempt="" color="" does="" everyone="" gets="" hat="" in="" least="" maximize="" n.="" not="" one="" or="" order:="" p="" pass.="" pass="" person="" prob="" right="" say="" that="" the="" their="" then="" they="" to="" want="" we="" who="" will="">There is a well known strategy where nobody passes which guarantees n-1 get it right (see <a href="http://blog.computationalcomplexity.org/2013/07/dump-your-tables-moral-of-my-story-that.html">here</a>), but that strategy has EVERYONE get it right 1/2 of the time. We want MORE than that. LOTS more.</n><br />
<n ...="" .="" 1="" 2="" and="" at="" attempt="" color="" does="" everyone="" gets="" hat="" in="" least="" maximize="" n.="" not="" one="" or="" order:="" p="" pass.="" pass="" person="" prob="" right="" say="" that="" the="" their="" then="" they="" to="" want="" we="" who="" will="">
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The following strategy works: For i=1,2,..., N person i does the following: if nobody has said RED yet AND ALL of the hats i sees are BLUE then i says RED. Otherwise Red passes<br />
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This fails on B^n. It works on everything else with the last R getting it right and everyone else passing. So the prob of getting it right is 1- 1/2^n.<br />
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POINT: I originally didn't have one to make, but a commenter misread the problem (or I miswrote it) in an interesting way. My problem was: Hats put on randomly, players are deterministic. They thought it was Hats put on by an adversary but players can use a randomized strategy. That problem (which frankly is more intersting) has a similar solution to the above: the players get a random string of R,B of length n and treat that like I treat B^n above.<br />
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2) omega people: 1,2,3,... and as above. We want to get all but a finite number of people get it right. See my writeup of it pointed to above. The proof I use uses the Axiom of choice and this is needed (see <a href="https://www.cs.umd.edu/users/gasarch/TOPICS/hats/infinite-hats-and-ac.pdf">here</a>).<br />
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POINT: some of my students didn't like that the players need uncountable memory. How much does this bother me: not even a little. A fellow blogger thought this result was so non-intuitive that he now thinks the axiom of choice is wrong (see <a href="https://cornellmath.wordpress.com/2007/09/13/the-axiom-of-choice-is-wrong/">here</a>) Personally I am a lot more bothered by the Banach Tarski Paradox (see <a href="http://blog.computationalcomplexity.org/2011/04/what-did-banachs-wife-think-of-banach.html">here</a>), though that paradox has lead to what my wife calls either the best or the most obscure math joke ever: what is an anagram of Banach-Tarski? Answer: Banach-Tarski Banach-Tarski.<br />
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3) omega people: 1,2,3,... and as above but now we want to get at most ONE wrong. You CAN do this! see the writeup.<br />
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POINT: When I first learned problem (2) I assumed you could not get it down to a finite bound. And I was sure I could prove it, though I never got around to it, prob because I thought it was true and easy. Well, my turn to eat humble pie (an expression only said on TV and not in real live)--- you CAN do this with only one error. The problem where you have an infinite number of people, they all see each others hats, and they all shout at the same time- that one I am sure you can't do with at most 1 error. I might need to eat humble pie once again.<br />
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4) n people, c colors, everyrone sees everyone else's hat, simul shouting, deterministic, and want to maximize how many get it right. OH- and adversarial.<br />
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Can do it with floor(n/c) but can't to better. See writeup.<br />
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POINT: The argument that you can't do better is a probabilistic argument! That's great! It may help bridge the gap between recreational and serious math (is there even a gap anymore?) that we use a Prob method on a fun hat problem! </n>GASARCHhttp://www.blogger.com/profile/06134382469361359081noreply@blogger.com1tag:blogger.com,1999:blog-3722233.post-8756043715849007432017-07-09T17:32:00.002-04:002017-07-10T13:45:13.425-04:00Two hat problems you may or may not have seen but I have a point to make about one of themHat problems are fun and often require clever solutions. I have posted about one type of hat problem <a href="http://blog.computationalcomplexity.org/2013/07/dump-your-tables-moral-of-my-story-that.html">here</a>.<span id="goog_836325510"></span><a href="https://www.blogger.com/"></a><span id="goog_836325511"></span><br />
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In this post I ask three. For two of them I have a point to make which I will make when I post the answer later in the week. Feel free to post your thoughts and answers, BUT be warned that if you don't want to know the answer then don't look at the comments.<br />
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1) N people stand in a line and are numbered 1,2,3,..,n. If i < j then person i can see person j's hat color.<br />
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Hats are going to be put on the heads RANDOMLY- prob of RED or BLUE is 1/2. (so no adversary)<br />
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The people, in order 1,2,3,..., n either say RED or BLUE or PASS.<br />
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We want to maximize the probability that (1) someone does not say PASS, and (2) ALL who do not say PASS are correct.<br />
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They can meet ahead of time to discuss strategy but after the hats are on ALL they can say<br />
is RED, BLUE, PASS and only when they are supposed to.<br />
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(Also try with 3 colors, 4 colors, etc.)<br />
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(ADDED LATER- some comments I got inspire a clarification and a new problem.<br />
<br />Clarify: NO adversary. The players are deterministic. So the prob of failure is based on the randomness of the hats. So you want to minimize the number of seq of R and B where the players mess up.<br />
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Another problem: Their IS an adversary but the players are allowed to flip coins. Now the prob of failure is based on the players coin flips.<br />
)<br />
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2) omega people in a line are numbered 1,2,3,... If < j then person i can see person j's hat color.<br />
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An ADVERSARY is going to put hats on peoples heads RED or BLUE.<br />
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The people in order 1,2,3,... either say RED or BLUE<br />
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They can meet ahead of time and discuss strategy as in problem 1. The Adversary KNOWS the strategy<br />
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a) Prove or Disprove: there is a protocol such that they always get all but a finite number of hats right<br />
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b) Prove or Disprove: there is a protocol such that they always get all but at most ONE right.<br />
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3) N people in a circle (so they see each others hats).<br />
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An Adversary is going to put hats on peoples heads- there are c hat colors.<br />
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The people AT THE SAME TIME shout out a hat color.<br />
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Give a protocol that maximizes how many get it right (in the worst case). Show there is no better protocol.<br />
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<br />GASARCHhttp://www.blogger.com/profile/06134382469361359081noreply@blogger.com6tag:blogger.com,1999:blog-3722233.post-50701599970376004112017-07-05T08:09:00.002-04:002017-07-05T08:09:47.305-04:00The Complexity of Rubik's Cube<div class="separator" style="clear: both; text-align: center;">
<a href="https://1.bp.blogspot.com/--bJ1YimqiRo/WVpXOqymEaI/AAAAAAABb2w/t2Y2235Byb4FFQZ4-Arw2XMx_gCM9MAnACLcBGAs/s1600/rubiks.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="188" data-original-width="170" src="https://1.bp.blogspot.com/--bJ1YimqiRo/WVpXOqymEaI/AAAAAAABb2w/t2Y2235Byb4FFQZ4-Arw2XMx_gCM9MAnACLcBGAs/s1600/rubiks.jpg" /></a></div>
In my book I use Rubik's Cube as an example of a puzzle we can computationally solve efficiently (as opposed to <a href="http://blog.computationalcomplexity.org/2005/05/complexity-and-sudoku.html">Sudoku</a> or <a href="http://blog.computationalcomplexity.org/2003/03/rush-hour.html">Rush Hour</a>). How does this square with the new <a href="https://arxiv.org/abs/1706.06708">result</a> of Erik Demaine, Sarah Eisenstat and Mikhail Rudoy that finding the shortest solution is NP-complete? New Scientist now proclaims <a href="https://www.newscientist.com/article/2139268-its-not-you-solving-a-rubiks-cube-quickly-is-officially-hard/">It’s not you – solving a Rubik’s cube quickly is officially hard</a>. No, it's still you.<br />
<br />
To study the complexity of Rubik's cube we can't just fixate on the 3x3x3 cube with its finite state space but on the general NxNxN cube. (One could also generalize to 3-sided hypercubes in N dimensions but good luck constructing a 3x3x3x3x3 Rubik's cube.) For a given mixed-up NxNxN cube we can find in polynomial time a polynomial number of steps to return the cube to the original state. A mixed-up cube is just a member of the permutation group of the 6N<sup>2</sup> small squares and we want to find a sequence of generators (allowable rotations of the cube) that yield the mixed-up cube. Group theorists have come up with <a href="http://www.cmi.ac.in/~ramprasad/lecturenotes/algcomp/lecture4.pdf">very efficient algorithms</a> to find these sequences which we can apply in reverse to solve the cube.<br />
<br />
Group theory does not necessarily come up with the shortest possible sequence and <a href="http://www.cube20.org/">only in 2010</a> did we discover that solving the worst-case 3x3x3 cube, the so-called "God's Number", required 20 moves. A year later Demaine et. al <a href="https://arxiv.org/abs/1106.5736">showed</a> that the minimum sequence for an NxNxN cube is Θ(N<sup>2</sup>/log N).<br />
<br />
Two weeks ago Demain, Eisenstat and Rudoy <a href="https://arxiv.org/abs/1706.06708">posted their proof</a> that given a fixed NxNxN cube finding the shortest sequence in NP-complete. Their proof is combinatorial, showing that solving an NxNx1 cube is NP-complete and reducing to the NxNxN cube.<br />
<br />
So there you have it, solving a generalized Rubik's cube is easy but finding the shortest possible solution is hard. Despite Rubik's Cube achieving popularity during my nerdy high school days, I never had the patience to solve it, but that's just me.Lance Fortnowhttps://plus.google.com/101693130490639305932noreply@blogger.com3tag:blogger.com,1999:blog-3722233.post-26354347206146872892017-06-29T10:09:00.002-04:002017-06-29T10:09:48.208-04:0050 Years of the Turing Award<div class="separator" style="clear: both; text-align: center;">
<a href="https://4.bp.blogspot.com/-40HMIPmxF_8/WVPDJXG08_I/AAAAAAABbzw/3vxn9IYHNl8hoYX9PFcZ1TcnuX44ZYBZgCKgBGAs/s1600/IMG_20170623_124232.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="150" src="https://4.bp.blogspot.com/-40HMIPmxF_8/WVPDJXG08_I/AAAAAAABbzw/3vxn9IYHNl8hoYX9PFcZ1TcnuX44ZYBZgCKgBGAs/s200/IMG_20170623_124232.jpg" width="200" /></a></div>
The ACM knows how to throw a party, a two-day <a href="https://www.acm.org/turing-award-50/conference">celebration</a> of the 50th anniversary of the Turing Award. Every recipient got a deck of <a href="https://twitter.com/fortnow/status/878280071366062080">Turing Award playing cards</a> and the ACM unveiled a new bust of Turing perfect for selfies.<br />
<br />
The conference featured a number of panels on different challenges of computer science from privacy to quantum. Deep Learning formed a common thread, not only did it have its own panel but the Moore's law panel talked about specialized hardware for learning and deep learning causes concern for the privacy and ethics panels. Even quantum computing used deep learning as an example of a technology that succeeded once the computing power was there.<br />
<br />
The deep learning panel focused on what it can't do, particularly semantics, abstraction and learning from a small or medium amount of data. Deep networks are a tool in the toolbox but we need more. My favorite line came from Stuart Russell worried about "Grad Student Descent", research focused on parameter tuning to optimize learning in different regimes, as opposed to developing truly new approaches. For the theory folks, some questions like how powerful are deep neural nets (circuit complexity) and whether we can just find the best program for some data (P v NP).<br />
<br />
The "Moore's Law is Really Dead" panel joked about the <a href="https://www.youtube.com/watch?v=npjOSLCR2hE">Monty Python parrot</a> (it's resting). For the future, post-CPU software will need to know about hardware, we'll have more specialized and programmable architectures and we'll have to rely on better algorithms for improvement (theory again). Butler Lampson said "The whole reason the web works is because it doesn't have to." I don't remember how that fit into the discussion but I do like the quote.<br />
<br />
The quantum panel acknowledged that we don't quite have the algorithms yet but we will soon have enough qbits to experiment and find ways that quantum can help.<br />
<br />
You can <a href="https://www.facebook.com/pg/AssociationForComputingMachinery/videos/">watch the panels</a> yourself, but the real fun comes from spending time with the leaders of the field, and not just theory but across computer science.Lance Fortnowhttps://plus.google.com/101693130490639305932noreply@blogger.com3tag:blogger.com,1999:blog-3722233.post-51514531560103342612017-06-26T09:24:00.000-04:002017-06-26T11:34:38.636-04:00Best. STOC. Ever.<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/-CyDinHchw2o/WVEC5SiHkVI/AAAAAAABbyE/b-QlCqtNdz0uZqtaGCNKkDGZEatzNB2_wCLcBGAs/s1600/IMG_20170621_085138.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="632" data-original-width="1600" height="156" src="https://2.bp.blogspot.com/-CyDinHchw2o/WVEC5SiHkVI/AAAAAAABbyE/b-QlCqtNdz0uZqtaGCNKkDGZEatzNB2_wCLcBGAs/s400/IMG_20170621_085138.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The Panel on TCS: The Next Decade</td></tr>
</tbody></table>
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Last week I attended <a href="http://acm-stoc.org/stoc2017/">STOC</a> as its first new TheoryFest in Montreal. Pretty much everything about TheoryFest went extremely well and for the first time in a long time I felt STOC played a role beyond a publication venue. Great plenary talks from both within and outside the community. The poster sessions were well-attended and caused our community to talk to each other--what a concept. Senior people took junior people to lunch--I had a great time with graduate students Dhiraj Holden (MIT) and Joseph Bebel (USC). I missed the tutorials and workshops but heard they went very well.<br />
<br />
By the numbers: 370 attendees, 46% students. 103 accepted papers out of 421 submitted. These numbers are moderate increases over recent years.<br />
<br />
The Panel on TCS: The Next Decade talked about everything but the next decade. A few of my favorite quotes: "Hard instances are everywhere except where people care" (Russell Impagliazzo, who walked back a little from it later in the discussion). "I never know when I proved my last theorem" (Dan Spielman on why he keeps trying). Generally the panel gave great advice on how to do research and talk with other disciplines.<br />
<br />
Avi Wigderson argued that theory of computing has become "an independent academic discipline" which has strong ties to many others, of which computer science is just one example. He didn't quite go as far as suggesting a separate department but he outlined a TCS major and argued that our concepts should be taught as early as elementary school.<br />
<br />
Oded Goldreich <a href="https://www.sigact.org/Prizes/Knuth/citation2017.pdf">received the Knuth Prize</a> and said that researchers should focus on their research and not on their careers. The SIGACT Distinguished Service Award <a href="https://www.sigact.org/Prizes/Service/2017.pdf">went to Alistair Sinclair</a> for his work at the Simons Institute.<br />
<br />
Oded apologized for lying about why he was attending STOC this year. TheoryFest will be a true success when you need reasons to not attend STOC. All happens again next year in Los Angeles (June 23-27) for the 50th STOC. Do be there.Lance Fortnowhttps://plus.google.com/101693130490639305932noreply@blogger.com1tag:blogger.com,1999:blog-3722233.post-59050634988290893062017-06-24T09:44:00.000-04:002017-06-24T09:44:01.646-04:00Joan Clarke (1917-1996)I'm in San Francisco for the <a href="https://www.acm.org/turing-award-50/conference">ACM conference celebrating 50 years of the Turing Award</a>. I'll post on <a href="http://acm-stoc.org/stoc2017/">STOC</a> and the Turing award celebration next week. Today though we remember another member of Bletchley Park, <a href="http://www-history.mcs.st-and.ac.uk/Biographies/Clarke_Joan.html">Joan Clarke</a>, born one hundred years ago today, five years and a day after Turing.<br />
<br />
Clarke became one of the leading cryptoanalysts at Bletchley Park during the second World War. She mastered the technique of Banburismus developed by Alan Turing, the only woman to do so, to help break German codes. Bletchley Park promoted her to linguist, even though she didn't know any languages, to partially compensate for a lower pay scale for woman at the time. Keira Knightly played Joan Clarke in <a href="http://www.imdb.com/title/tt2084970/">The Imitation Game</a>.<br />
<br />
Joan Clarke had a close friendship with Turing and a brief engagement. In this <a href="https://youtu.be/MB2e9R7bXCk">video</a> Joan Clarke talks about that time in her life.<br />
<br />
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<iframe allowfullscreen="" frameborder="0" height="315" src="https://www.youtube.com/embed/MB2e9R7bXCk" width="560"></iframe></center>
Lance Fortnowhttps://plus.google.com/101693130490639305932noreply@blogger.com0tag:blogger.com,1999:blog-3722233.post-70926151273024594822017-06-20T16:21:00.003-04:002017-06-20T23:35:56.665-04:00Harvard revokes admission of students based on what was said in a private(?) chat roomHarvard revoked the admission of 10 students (see <span id="goog_1709924099"></span><a href="https://www.blogger.com/"></a><span id="goog_1709924100"><span id="goog_1646697970"></span><a href="https://www.blogger.com/"></a><span id="goog_1646697971"><a href="https://www.usnews.com/news/national-news/articles/2017-06-05/harvard-pulls-student-admission-offers-after-explicit-facebook-posts">here</a>) based on what the students said in a private (can't have been too private) chat room.</span></span><br />
<br />
(ADDED later upon reflection- Harvard has only confirmed that there is a clause students are made<br />
aware of about immaturity and moral character. As for the reason for the revoking- we only have<br />
what is reported and that comes from the students. Are the students trustworthy on this? Given that they are being expelled for moral reasons... But more seriously we really don't' know. I just want to caution that we do not know the full story and never will. Note that Harvard is not legally allowed to disclose why they revoked, while the students can say what they want. For an example of how off a reported story can be see <a href="https://fivethirtyeight.com/features/leaving-social-media-taught-me-how-broken-the-news-cycle-is/">this</a> though I am sure you all know other examples.)<br />
<br />
Normally I would be aghast (and I may still be aghast) because of the slippery slope:<br />
<br />
Today you revoke admissions because students mock sexual assault, the Holocaust, and the death of children, and call the hypothetical hanging of a Mexican child ``pinata time''<br />
<br />
Tomorrow you revoke admissions because a student is a Trump Supporter. (Readers: I assume that you would find revoking admission because a student is a Trump supporter to be disgusting and absurd.)<br />
<br />
I felt strongly against this and sought out some other viewpoints. Here are some:<br />
<br />
1) Harvard is within their rights to do this legally according to what they agree to when they accept you. This is true. This is also irrelevant- I am interested in if its the right thing to do, not if its legal.<br />
<br />
2) The content of the chat rooms indicates a lack of moral character. This is a stronger argument. However the nebulousness of ``moral character'' reminds me of the origin of taking moral character into account: it was an excuse to let in less Jews (see the book t Harvard, Yale, and Princeton, see <i>The Chosen: The hidden history of admissions and exclusion a</i> review <a href="http://www.nytimes.com/2005/11/06/books/review/the-chosen-getting-in.html">here</a>). Jews do not have less moral char, but it was used as an excuse to admit less of them. Even though in the case at hand moral char is a legit issue, the history of the use of this issue bothers me. Slippery slope again.<br />
<br />
3) For crying out loud bill, LIFE is a Slippery Slope! You have to draw the line somewhere! And wherever you draw it, these kids are over that line. This argument, combined with the moral-point of item 2, I do find compelling.<br />
<br />
4) Here is a one border (I do not know if it was crossed): If a student personally attacks another student then this is grounds for revoking. Sounds good but what constitutes a personal attack?<br />
<br />
Counter argument: : Whenever a disgusting point of view is censored or punished the conversation shifts from<br />
<br />
That is a disgusting point of view<br />
<br />
to<br />
<br />
Free Speech! Oppressing unpopular views!<br />
<br />
I would rather the conversation be about why the point of view is wrong (or disgusting) rather than on Free Speech.<br />
<br />
Right now I am 75% against the revoking of the students admissions. This has no effect- I am not in any position of power, I won't give less money to Harvard (I am an alum-Grad school, which is why I noticed the story in the first place). I find the question interesting and,<i> more than usual</i>, welcome your comments. Based on your comments that 75 might change! In either direction!GASARCHhttp://www.blogger.com/profile/06134382469361359081noreply@blogger.com24tag:blogger.com,1999:blog-3722233.post-14525538557067967892017-06-14T09:23:00.000-04:002017-06-14T09:23:13.816-04:00The Power of Economic InefficiencyI grew up in a time when long distance domestic phone calls from AT&T costed $0.20/minute off peak ($1.30 in today's dollars). I also grew up close to AT&T Bell Labs, a mecca that claimed more PhDs than any university many doing independent research. Now I get all the phone minutes I can use and Bell Labs is a tiny fraction of what it once was. Was it a good trade?<br />
<br />
Technology has helped eliminate many of the economic inefficiencies. Usually for the better but sometimes these inefficiencies has good side effects. For another example take airlines--we can now so easily compare airlines on price so they often compete on price at the cost of service. Don't even get me started on newspapers.<br />
<br />
Universities remain one of the institutions where technological change has not had the cost savings effect that we've seen in communication and transportation. That's one of the reasons that universities have become more expense. We can't keep raising tuition and being pushed to focus on eliminating inefficiencies, seeking new ways to deliver classes for example. Will the research university as we know it survive?Lance Fortnowhttps://plus.google.com/101693130490639305932noreply@blogger.com6tag:blogger.com,1999:blog-3722233.post-80095960983785921882017-06-12T11:29:00.000-04:002017-06-12T14:31:34.309-04:00Climate Change: The Evolution of the Deniers/Does Paul Ryan Hate His Grandchildren?<br />
I went to the Mach for Science and then Drumpf pulled out of the Paris Accords. Causation or Correlation? I then posted about climate change (CC). That's caustation.<br />
<br />
1) Deniers:<br />
<br />
The deniers have gone through several phases:<br />
<br />
There is no CC<br />
<br />
There is CC but its not caused by humans.<br />
<br />
There is CC and its caused by humans but since China and India and other countries aren't doing anything about it, if only we do it will have no effect except to ruin our economy.<br />
(Counter argument: the effects of climate change are economically devastating- are insurance companies trying to pressure governments to do something about CC since CC's effects cause damage which hurts their bottom line?)<br />
<br />
Intermixed with these arguments have been:<br />
<br />
Just because 87% of all lung cancer victims smoke, that's just a correlation. Maybe people the lung cancer gene is also the smoking gene. Correlation does not equal causation. OH, sorry, that's a flashback to the Correlation NOT causation arguments made by the Tobacco companies. Do they still believe that? Mike Pence does (see <a href="https://thinkprogress.org/mike-pence-cigarette-truther-4b89e9304759">here</a>). How can they stay in business? (<a href="https://www.youtube.com/watch?v=6UsHHOCH4q8">here's how</a>) ANYWAY, some are making the correlation NOT causation argument for why Polar bears are dying, etc.<br />
<br />
AND the classic<br />
<br />
Technology will bail us out. (This would be a better argument if it was followed by <i>hence we wil</i>l <i>give lots of funding for such technology</i> which is NEVER what its followed by.)<br />
<br />
OKAY, so where are we in 2017?<br />
<br />
The economist had an argument about how Solar and Wind will soon be MORE cost effective than Oil and Gas- though we still have the problem of what happens on a cloudy, windless day- so we need technology to store (see <a href="http://www.economist.com/news/leaders/21717371-thats-no-reason-governments-stop-supporting-them-wind-and-solar-power-are-disrupting">here</a> though its behind a pay wall). China and India ARE doing things about CC. How much? Effective? Hard to say- though both are really concerned with pollution.<br />
<br />
I predict the new argument will be:<br />
<br />
We're all doomed anyway so why take our economy down at the same time.<br />
<br />
Unfortunately this argument might be correct.<br />
<br />
(ADDED LATER- a commenter says that I conspicuously left out religious arguments to not do anything about CC. I now conspicuously ask you to read his comment.)<br />
<br />
2) Take Paul Ryan. Please.<br />
Seriously-- I assume he KNOWS that CC really is a problem and the longer we put it off the worse it will be for his grandchildren, and perhaps his children. So why does he fight ANY attempt to even admit we HAVE a problem (And note there ARE some market-based solutions- a Carbon Tax, Cap and Trade.) Some speculation<br />
<br />
a) Despite being smart he's in deep deep denial. Okay, but why is that? If you believe in small government then if something comes along that REQUIRES big government, you just DENY it since it does not fit into your world view.<br />
<br />
b) Paul Ryan hates his Grandchildren.<br />
<br />
c) Paul Ryan thinks that HIS grandchildren will be among the few people who survive and live in a VERY gated community. He's probably wrong about that as even those in gated communities will suffer the effects of CC.<br />
<br />
d) Paul Ryan is stuck. If he tries to do ANYTHING then it will not work AND he'll lose his speakership and possibly his seat in congress. And there are a large number of congressman and senators who feel the same way but they're all afraid to say. If they ALL said so then... they'd ALL lose their seat in congress. One of the downsides of politics is ending up STUCK on the WRONG side of history and KNOWING it. Well, at least there won't be much history left so he won't be stuck on the wrong side for long.<br />
<br />
3) Game Theory. I used to think that it was in NO countries SHORT term interest to do anything serious about CC (that is, do it alone) and hence we were all DOOMED! Doomed I say! And part of the problem is that if Country A emits greenhouse gases its bad for THE ENTIRE WORLD EQUALLY, and not for Country A in particular. But a few things make me more optimistic:<br />
<br />
Pollution is a here-and-now problem for China and India so they will tackle that. That somehow has to be part of the solution.<br />
<br />
Technology- as mentioned before Solar and Wind is catching up to Gas and Oil. (downside of technology- Fracking and oil extraction are also getting better and cheaper. <a href="https://en.wikipedia.org/wiki/Hubbert_peak_theory">Hubbert's Peak Oil Theory</a> doesn't seem to be true) But the real advantage of Solar and Wind will be that you don't have to Extract and ship Oil (or Coal or whatever).<br />
<br />
4) I wrote that last positive point before President Drumpf. Having a CC denier in the white house means four more years of no action which sounds really bad- especially since the longer we put off doing something about the problem, the harder and more expensive it will be to slow down CC (Some ponders that Trump won't be that bad for the environment: <a href="https://fivethirtyeight.com/features/a-weaker-epa-may-not-mean-the-environment-goes-to-hell/">here</a>)<br />
<br />
5) Okay Bill, what would YOU do? Carbon Tax will give financial incentive for companies to curb Carbon emissions. And its simple. The Tax has to be high enough to have an effect. Another added bonus will be to help America pay down its deficit. ALSO more research into renewables. Oddly enough I would also recommend NOT forcing Gas to contain Ethanol- make Ethanol compete with Solar and Wind. (Recall that Ethanol is funded only because of the Iowa Caucus. If you don't know what I'm talking about, don't worry, its too stupid to explain.) Some may disagree and have other ideas. Thats FINE- I would rather be having a debate about what to DO about the problem rather than one about whether or not there IS a problem. Though even a debate about what to do about the problem should be SHORT so we can begin DOING something.<br />
<div>
<br /></div>
GASARCHhttp://www.blogger.com/profile/06134382469361359081noreply@blogger.com5tag:blogger.com,1999:blog-3722233.post-91879534097249510932017-06-08T08:17:00.000-04:002017-06-08T08:18:10.210-04:00Theory Jobs 2017In the fall we <a href="http://blog.computationalcomplexity.org/2016/10/2016-fall-jobs-post.html">point to theory jobs</a>, in the spring we see who got them. Like <a href="http://blog.computationalcomplexity.org/2016/05/theory-jobs-2016.html">last year</a> and years past I created a fully editable <a href="https://docs.google.com/spreadsheets/d/1xBpgBZXcSxjEAbU7SYCeXOJOJtPeXYCOFArqL28Uho8/edit?usp=sharing">Google Spreadsheet</a> to crowd source who is going where. Ground rules:<br />
<ul>
<li>I set up separate sheets for faculty, industry and postdoc/visitors.</li>
<li>People should be connected to theoretical computer science, broadly defined.</li>
<li>Only add jobs that you are absolutely sure have been offered and accepted. This is not the place for speculation and rumors.</li>
<li>You are welcome to add yourself, or people your department has hired.</li>
</ul>
This document will continue to grow as more jobs settle. So check it often.<br />
<br />
<iframe frameborder="0" height="750" src="https://docs.google.com/spreadsheets/d/1xBpgBZXcSxjEAbU7SYCeXOJOJtPeXYCOFArqL28Uho8/pubhtml?widget=true&headers=false" width="575"></iframe>
<a href="https://docs.google.com/spreadsheets/d/1xBpgBZXcSxjEAbU7SYCeXOJOJtPeXYCOFArqL28Uho8/edit?usp=sharing">Edit</a>
Lance Fortnowhttps://plus.google.com/101693130490639305932noreply@blogger.com14tag:blogger.com,1999:blog-3722233.post-89756049574637317802017-06-05T18:09:00.004-04:002017-06-20T18:56:27.158-04:00Big News on W(3,r) !This is a JOINT POST with Evangelos Georgiadis who brought this problem to my attention.)<br />
<br />
In 2010 I posted about how dense a set of integers has to be before you know there is a 3-AP in it (a 3-AP is a set of three numbers equally spaced). Such results were motivated by and are applied to getting upper bounds on<br />
<br />
W(3,r) = the least W such that any r-coloring of {1,...,W} has a monochromatic 3-AP.<br />
<br />
That blog, which also has history and context, is <a href="http://blog.computationalcomplexity.org/2010/12/breakthrough-result-on-density-and-3.html">here</a><br />
<br />
At the time of that post the following was known (and had just been proven by Sanders <a href="https://arxiv.org/abs/1011.0104">see here</a>)<br />
<br />
If A ⊂ {1,...,N} and |A| ≥ N*(log log N)<sup>5</sup> / log N then A has a 3-AP<br />
<br />
and hence<br />
<br />
W(3,r) ≤ 2<sup>r(log r)<sup>5</sup></sup><br />
<br />
<br />
<br />
<br />
<sup><br /></sup>
(Added later: Bloom's paper (see link on next line) reports that Sanders result is a bit weaker than claimed- the 5's should be 6's, calculation error.)<br />
<br />
This has now been improved!. Thomas Bloom, in <a href="https://arxiv.org/abs/1405.5800">this paper</a> has shown<br />
<br />
If A ⊂ {1,...,N} and |A| ≥ N*(log log N)<sup>4</sup> / log N then A has a 3-AP<br />
<br />
and hence<br />
<br />
W(3,r) ≤ 2<sup>r(log r)<sup>4</sup></sup><br />
<br />
An easy prob argument gives<br />
<br />
W(3,r) ≥ r<sup>3/2</sup><br />
<br />
<br />
So is W(3,r)'s growth rate poly? Exp? in between? Is there a connection to SAT?<br />
<br />
One can phrase the question <i>W(k,r)=m</i> as asking of a certain Boolean Formula is it satisfiable. IF we can get theorems about that kind of formula, that might help.<br />
<br />
However, I doubt that it has much real connection to the general SAT problem.<br />
<br />
I don't know if the consensus of the community is that W(3,r) is poly or exp.<br />
<br />
(Warning: I've seen W(3,r) to mean something else: W(3,r) is the least W such that any 2-coloring of {1,...,W} with colors 0 and 1 has either a 0-colored 3-AP or a 1-colored k-AP. This is NOT the function we are talking about, though that one is also interesting. )<br />
<br />
ADDED LATER: Knuth's Volume 4, Fascicle 6 has theorems about this W(3,r)<br />
<br />
ADDED LATER: A commenter said that a simple prob greedy algorithm using salem-spencer sets<br />
yields<br />
<br />
W(3,r) ≥ exp(C (ln r)<sup>2</sup>)<br />
<br />
I reconstructed the proof from these comments, though using Behrends sets instead of SS<br />
<br />
The proof is here: <a href="https://www.cs.umd.edu/users/gasarch/BLOGPAPERS/w3r.pdf">here</a><br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />GASARCHhttp://www.blogger.com/profile/06134382469361359081noreply@blogger.com5tag:blogger.com,1999:blog-3722233.post-60686214555433200512017-06-01T10:01:00.001-04:002017-06-01T10:01:29.516-04:00Who Sets Policy?In April the New York Times Magazine ran an article <a href="https://www.nytimes.com/2017/04/18/magazine/is-it-ok-to-engineer-the-environment-to-fight-climate-change.html">Is it O.K. to Tinker with the Environment to Fight Climate Change?</a> The article asks about the ethics of even running tests on such methods and has this quote froms David Battisti, an atmospheric scientist at UW.<br />
<blockquote class="tr_bq">
Name a technology humans have developed that they haven't used. I can't think of any. So we can work on this for sure. But we are in this dilemma: Once we do develop this technology, it will be tempting to use it.</blockquote>
The article skirts the question on who makes this decision. Maybe the United Nations after some unlikely agreement among major powers. But what if the UN doesn't act and some billionaire decides to fund a project?<br />
<br />
As computer scientists we start to face these questions as software in our hyper-connected world starts to change society in unpredictable ways. How do we balance privacy, security, usability and fairness in communications and machine learning? What about net neutrality, self-driving cars, autonomous military robots? Job disruption from automation?<br />
<br />
We have governments to deal with these challenges. But the world seems to have lost trust in its politicians and governments don't agree. How does one set different rules across states and countries which apply to software services over the Internet?<br />
<br />
All too often companies set these policies, at least the default policies until government steps in. Uber didn't ask permission to completely change the paid-ride business and only a few places pushed back. Google, Facebook, etc. use machine learning with abandon, until some governments try and reign them in. The Department of Defense and the NSA, in some sense industries within government, set their policies often without public debate.<br />
<br />
What is our role as computer scientists? It's not wrong to create the technologies, but we should acknowledge the ethical questions that come with them and what we technically can and cannot do to address them. Keep people informed so the decision makers, whomever they be, at least have the right knowledge to make their choices.Lance Fortnowhttps://plus.google.com/101693130490639305932noreply@blogger.com3tag:blogger.com,1999:blog-3722233.post-42015423151511964702017-05-30T11:33:00.000-04:002017-05-30T11:35:06.123-04:00Google Scholar thinks my Hilbert Number is 1(I want to thank Lane Hemaspaandra for bringing this to my attention.)<br />
<br />
When I google:<br />
<br />
google scholar William Gasarch<br />
<br />
I get <a href="https://scholar.google.com/citations?user=SVRgMwEAAAAJ&hl=en">this </a><br />
<br />
(I wonder if what you get depends on who you are- I describe below what I get.)<br />
<br />
The first entry on it is<br />
<br />
<i>Methods of Mathematical Physics</i> by Courant and Hilbert.<br />
<br />
The first page page that Google brings up has all papers with Hilbert as a co-author except the book<br />
<br />
<i>Handbook of discrete and combinatorial mathematics </i>edited by Rosen<br />
<br />
I have a short article in that book.<br />
<br />
The second page has the paper of Hilbert:<br />
<br />
<i>Uber die irreducible ganzer rationaler blah blah</i><br />
<i><br /></i>
which I have a connection to since Mark Villarino, Bill Gasarch, and Ken Regan have a paper explaining this paper in modern terms <a href="https://arxiv.org/abs/1611.06303">here</a>. Could this have confused google scholar into thinking I am Hilbert? Seems unlikely.<br />
<br />
In fact, the first two pages are all papers with Hilbert as an author. The third page has<br />
<br />
<i>Some connections between bounded query classes and non-uniform complexity</i> by Amir, Beigel, Gasarch.<br />
<br />
And after that the pages are a mix of Hilbert's papers and mine, though mostly his since he had so many more papers than I did.<br />
<br />
This raises some questions<br />
<br />
1) How did this happen? Did I hack google scholar? Many theorists at one time in their lives were excellent programmers- however, I am not one of them.<br />
<br />
2) How common is it for google scholar to be this far wrong?<br />
<br />
3) If I wanted to get this fixed who would I tell? In the past whenever I've tried to tell a company something FOR THEIR OWN GOOD I get the same run-around as when I am trying to get information not on their website, so I have STOPPED even trying. Same here?<br />
<br />
4) Should I want to get it fixed? I am proud to be affiliated with Hilbert!GASARCHhttp://www.blogger.com/profile/06134382469361359081noreply@blogger.com2tag:blogger.com,1999:blog-3722233.post-306869909666094772017-05-25T08:31:00.002-04:002017-05-25T08:35:37.366-04:00Graduation from the Other Side<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://1.bp.blogspot.com/-yLeNCtLuUJ4/WSbLYz7IpmI/AAAAAAABbJs/OMIKdWTM7m8n8i3X4uyNTcInsusj6EMlgCKgB/s1600/IMG_20170521_124205.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="150" src="https://1.bp.blogspot.com/-yLeNCtLuUJ4/WSbLYz7IpmI/AAAAAAABbJs/OMIKdWTM7m8n8i3X4uyNTcInsusj6EMlgCKgB/s200/IMG_20170521_124205.jpg" width="200" /></a></div>
<a href="http://www.brandeis.edu/now/2017/may/images/lamport620x413.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://www.brandeis.edu/now/2017/may/images/lamport620x413.jpg" data-original-height="413" data-original-width="620" height="132" width="200" /></a><br />
I've attended many graduations in my time, mostly as faculty, a couple of times as a student or a brother. This last weekend I attended my first university graduation as a parent as my daughter Annie graduated from Brandeis University in Waltham, Massachusetts. Brandeis has a big graduation ceremony with lots of speeches and then different departments or groups of departments have their own diploma ceremonies with their own speakers and where they give out the actual diplomas.<br />
<br />
Brandeis gives out a number of <a href="http://www.brandeis.edu/commencement/honorees/index.html">honorary doctorates</a> each year and for the first time gave one to a computer scientist, Turing Award Winner <a href="http://www.brandeis.edu/commencement/honorees/lamport.html">Leslie Lamport</a>. Lamport received his PhD at Brandeis in math in 1972 before they had a CS deparment but now he has an (honorary) PhD in Computer Science. Lamport gave an <a href="http://www.brandeis.edu/now/2017/may/commencement-lamport.html">eight-minute talk</a> in the School of Science ceremony. But when you are a parent the weekend is about your child and my daughter didn't graduate from the school of science so I didn't see the Lamport talk.<br />
<br />
In the main ceremony, Brandeis has not only an undergrad give a speech but also a grad student. Sounds like a crazy idea, but Vivekanand Vimal, Neuroscience PhD, gave what could be best described as a performance art. Since I can't find the video of Lamport and you probably don't want to see my videos of Annie, enjoy the new Dr. Vimal's <a href="https://youtu.be/qHOpn8z3UVs">ode to the craziness of the PhD and saving society</a>.<br />
<br />
<iframe allowfullscreen="" frameborder="0" height="315" src="https://www.youtube.com/embed/qHOpn8z3UVs" width="560"></iframe>Lance Fortnowhttps://plus.google.com/101693130490639305932noreply@blogger.com1tag:blogger.com,1999:blog-3722233.post-79842355369995715552017-05-18T08:42:00.002-04:002017-05-18T08:42:53.204-04:00The Optimizers<div class="separator" style="clear: both; text-align: center;">
<a href="http://pwp.gatech.edu/nem-fest-2017/wp-content/uploads/sites/511/2016/09/Nems4.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://pwp.gatech.edu/nem-fest-2017/wp-content/uploads/sites/511/2016/09/Nems4.png" height="320" width="200" /></a></div>
Last week the Georgia Tech School of Industrial and Systems Engineering honored the 80th birthday of George Nemhauser and the 70th of Arkadi Nemirovski at an event naturally called <a href="https://pwp.gatech.edu/nem-fest-2017/">NemFest</a>. The Nems are powerhouses in the optimization community and this event drew many of the greats of the field.<br />
<br />
In theoretical CS we often take NP-complete as a sign to stop searching for an efficient algorithm. Optimization people take NP-complete as a starting point, using powerful algorithmic ideas, clever heuristics and sheer computing power to solve or nearly optimize in many real-world cases.<br />
<br />
Bill Cook talked about his adventures with the traveling salesman problem. Check out his <a href="https://www.theguardian.com/travel/2016/oct/21/worlds-longest-pub-crawl-maths-team-plots-route-between-every-pub-in-uk">British pub crawl</a> and <a href="http://www.math.uwaterloo.ca/tsp/us/index.html">his tour</a> through the nearly 50,000 US historic sites.<br />
<br />
<a href="http://mat.tepper.cmu.edu/trick/">Michael Trick</a> talked about his side job, schedule MLB baseball games, a surprisingly challenging problem. Like TSP, you want to minimize total travel distance but under a wide variety of constraints. "There's something satisfying about being at a bar, seeing a game on the TV and knowing those two teams are playing because you scheduled them." Can't say I've had that kind of satisfaction in my computational complexity research.Lance Fortnowhttps://plus.google.com/101693130490639305932noreply@blogger.com1tag:blogger.com,1999:blog-3722233.post-66444503803321642102017-05-16T09:28:00.002-04:002017-05-17T09:27:41.971-04:00If an ugrad asks `is field X worth studying' the answer is almost always yesAn undergraduate Freshman recently emailed me that he was very interested in Quantum Computing and wanted to know<br />
<br />
1) Who on the fCS aculty works in QC (Answer: Andrew Childs though you should ask him about postdocs, grad students, and Physics faulty in the area.)<br />
<br />
2) What are good books on QC for a bright ugrad. I said the following:<br />
<br />
QC since Democritus by Aaronson<br />
QC-A gentle introduction by Rieffel and Polak<br />
QC for CS by Yanofsy and Mannucci<br />
QC and QI by Nielsen and Chuang<br />
Some of Scott's blog posts.<br />
Ask Andrew Childs for more.<br />
<br />
my webpage of book reviews for SIGACT NEWS <a href="https://www.cs.umd.edu/~gasarch/bookrev/bookrev.html">here</a> and search for Quantum to get some other books- read the reviews and pick one.<br />
<br />
on Amazon type in quantum computing and see what reviews say- though they might not be reliable.<br />
<br />
There are likely other good books but I do not know of them. (You can leave comments.)<br />
<br />
3) Is QC a good topic to get into? I said YES of course. My reasoning is that they would of course LEARN something by studying it.<br />
<br />
But this raises the question: When would I say `that field is not worth studying' ?<br />
<br />
1) If they really want to do RESEARCH and the topic is either too dead or too hard and they want to actually do research (as opposed to learning the topic without wanting to to research).<br />
<br />
2) If there was nobody around to help them in that topic. Might still be okay if they are both highly motivated and very smart.<br />
<br />
3) If the topic was bogus AND they would learn NOTHING from studying it. Are there topics that are bogus but you still learn from studying them? Does studying astrology seriously teach you some astronomy? Some history? How about Alchemy and Chemistry? Fine if the students KNOWS that Astrology is bogus and Alchemy is not correct.<br />
<br />
The points is that I really do not want to dampen someone's enthusiasm for a topic.<br />
<br />
SO- aside from the reasons above, can you think of any other reason to discourage a student from a topic they are interested in? I ask, as always, non-rhetorically.<br />
<br />
<br />
<br />GASARCHhttp://www.blogger.com/profile/06134382469361359081noreply@blogger.com4tag:blogger.com,1999:blog-3722233.post-8899794188639699302017-05-14T09:18:00.000-04:002017-05-14T09:24:31.229-04:00William Tutte (1917-2002)<div class="separator" style="clear: both; text-align: center;">
</div>
<a href="https://4.bp.blogspot.com/-FaiXLie1gbE/WRMpJ9LzYlI/AAAAAAABajk/LxPQrR0hm20uTZ_SCZUSQ-ucZ-dZwkBqwCLcB/s1600/bill-tutte4412-620x354.gif" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="183" src="https://4.bp.blogspot.com/-FaiXLie1gbE/WRMpJ9LzYlI/AAAAAAABajk/LxPQrR0hm20uTZ_SCZUSQ-ucZ-dZwkBqwCLcB/s200/bill-tutte4412-620x354.gif" width="200" /></a>Today we celebrate our mothers of course, but also the 100th anniversary of the birth of <a href="http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Tutte.html">Bill Tutte</a>, best known for his role in <a href="https://cacm.acm.org/magazines/2017/1/211102-colossal-genius/fulltext">decrypting the Lorenz cipher</a> used by the Nazi high command. Tutte also made many important advances in <a href="https://en.wikipedia.org/wiki/W._T._Tutte#Research_contributions">graph theory and algorithms</a>.<br />
<br />
For this post, let's look at one very powerful concept, the <a href="http://mathworld.wolfram.com/TuttePolynomial.html">Tutte Polynomial</a>, with a rather technical looking definition. Fix a graph G with vertex set V and edge set E with n = |V|. For a subset A of E, let k<sub>A</sub> be the number of connected components of A and n<sub>A</sub> be the number of vertices of the vertices of G induced by A, and k=k<sub>E</sub> the number of connected components of G.<br />
<br />
The Tutte polynomial T(x,y) is the sum over all subsets A of E of the quantity<br />
<div style="text-align: center;">
(x-1)<sup>k<sub>A</sub>-k</sup>(y-1)<sup>K<sub>A</sub>+n<sub>A</sub>-n</sup>.</div>
<div style="text-align: center;">
<br /></div>
<div style="text-align: left;">
What makes this problem interesting? For some fixed values of x and y we get various properties of the graph.</div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
T(2,1) is the number of forests of G.</div>
<div style="text-align: left;">
T(1,2) number of spanning forests (or spanning trees if G is connected.</div>
<div style="text-align: left;">
T(2,0) is the number of spanning subgraphs.</div>
<div style="text-align: left;">
T(0,2) is the number of strongly connected orientations.</div>
<div style="text-align: left;">
The value (-1)<sup>n-k</sup>q<sup>k</sup>T(1-q,0) counts the number of q-colorings of G.<br />
<br />
Computing T can be difficult. Counting the number of 3-colorings is #P-complete, equivalent to counting the number of satisfying assignments of a Boolean formula. So even computing T(-2,0) for a given graph G is #P-complete. Leslie Goldberg and Mark Jerrum <a href="http://dx.doi.org/10.1007/978-3-642-31594-7_34">show</a> that even computing the sign of a Tutte polynomial, just determining whether it is positive, zero or negative, on certain values is still #P-hard.<br />
<br />
This is only a sampling of the many <a href="https://en.wikipedia.org/wiki/Tutte_polynomial#Specialisations">applications</a> of the Tutte polynomial. Let's remember Tutte for creating a single function that captures so much information about a graph and helping to defeat the Nazis. Not a bad life. Must have had a good mother.</div>
Lance Fortnowhttps://plus.google.com/101693130490639305932noreply@blogger.com3tag:blogger.com,1999:blog-3722233.post-27568994052114358332017-05-11T09:07:00.000-04:002017-05-11T09:07:37.324-04:00How to Solve It<i>Today a guest post from <a href="http://papakons.business.rutgers.edu/">Periklis Papakonstantinou</a>, coincidentally not unrelated to Bill's <a href="http://blog.computationalcomplexity.org/2017/05/students-try-to-memorize-rather-than.html">post</a> earlier this week. I'll be back with a special post on Sunday.</i><br />
<br />
I'm teaching in an undergrad program that is half computer science and half business at Rutgers, but the CS part taught there is the real thing (I assume for Business too). This term I taught a very theoretical course in cryptography and I realized that (1) the students enjoyed it and (2) that they were lacking basic reasoning skills. I ended up teaching for a few weeks how one can structure basic logic arguments. I am not sure if they appreciated things like the hybrid argument but I believe I convinced them that without rigorous thinking one cannot think clearly.<br />
<br />
So, I decided to teach a much more fun class (hopefully next year) titled "How to solve it" -- à la Pólya. The goal is students to develop rigorous problem-solving skills. At the same time, I'd like to use this course as an excuse to introduce basic concepts in combinatorics, linear algebra, and theoretical stats. I'm not sure whether the original book by Polya is appropriate for this and that's why I thought of reaching out to my peers for suggestions. Any ideas and thoughts on possible texts, topics, or notes would be greatly appreciated.Lance Fortnowhttps://plus.google.com/101693130490639305932noreply@blogger.com5tag:blogger.com,1999:blog-3722233.post-50719858728243925802017-05-07T21:38:00.002-04:002017-05-08T08:54:53.959-04:00Students try to memorize rather than understand! Who knew! (everyone)<br />
Discrete Math. Required for CS majors, taken mostly by Sophmores. Goal is to teach them how to think rigorously. Topics are logic, number theory (not much), induction, sets, functions, relations, combinatorics (includes Pigeon hole prin, henceoforth PNP), prob, countability, uncountability.<br />
<br />
We taught the Pigeon Hole Principle and gave MANY examples and HW of the following type:<br />
<br />
Let A be a subset of {1,...,50} of size 10. Show there are two subsets of A that have the same sum.<br />
<br />
ANSWER: There are 2^{10} = 1024 possible subsets.<br />
<br />
MAXSUM is 41+..+50 = (1+...+ 50 )-(1 +...+ 40) = 50*51/2 - 40*41/2 = 455<br />
<br />
MINSUM is 0 (the empty set). So the NUMBER OF SUMS is 456<br />
<br />
Since 1024 > 456 there are two subsets of A of the same size.<br />
<br />
The EXAM covered PHP, combs, prob, and induction. Hence they should know n choose k<br />
<br />
On the HW and in class we NEVER did a problem where we only cared about the subsets of a fixed size. Conceptually this is really the same problem but if you had MEMORIZED the proof template and tried to apply it you would get it wrong.<br />
<br />
I asked the following on the exam: which was worth 20 points.<br />
<br />
(20 points) Let A be a subset of {1,...,21} of size 8. Show that A has at least two subsets of size 3 which have the same sum.<br />
<br />
ANSWER: There are (8 choose 3) = 56 subsets of A of size 3.<br />
MAXSUM = 19+20+21 = 60, MINSUM = 1+2+ 3 = 6,<br />
So the NUMBER OF SUMS is 60-5 = 55.<br />
<br />
Since 56> 55 there are two subsets of A of size 3 that have the same size.<br />
<br />
Grading rubric:<br />
<br />
If they got (8 choose 3) thats 3 points.(Many said 2^8- I suspect incorrect memorization)<br />
<br />
If they got the MAXSUM and the MINSUM both right (aritj errors- NO penalty) then 3 points<br />
(Many had MINSUM=0- I suspect incorrect memorization).<br />
<br />
If they knew to use these PHP then 3 points.<br />
<br />
If they got all three right then 20 points<br />
<br />
So they got 0,3,6, or 20.<br />
<br />
Here is the final tally:<br />
<br />
0 points: 85<br />
<br />
3 points: 190<br />
<br />
6 points: 71<br />
<br />
20 points: 167<br />
<br />
(For the entire exam: 39 100's, 55 90-99, 77 80-89, 77 70-79, 76 60-69, 70 50-59, 47 40-49, 24 30-39, 24 30-39, 17 20-29, 3 10-19, 3 1-9)<br />
<br />
This all raises the much harder question- how can we get students to UNDERSTAND rather than MEMORIZE<br />
<br />
Telling them: DO NOT MEMORIZE! TRY TO UNDERSTAND!- I did this. Oh well.<br />
<br />
Allowing a cheat sheet (which I did) is both good and bad for this issue.<br />
<br />
Giving them a much wider variety of problems of this type. Either they would understand OR they would memorize several different templates.<br />
<br />
I WELCOME your thoughts on either my grading or on how to get them to try to UNDERSTAND rather than MEMORIZE.<br />
<div>
<br /></div>
<br />GASARCHhttp://www.blogger.com/profile/06134382469361359081noreply@blogger.com43tag:blogger.com,1999:blog-3722233.post-35269903637347313222017-05-04T08:12:00.003-04:002017-05-04T08:12:49.640-04:00Summer ConferencesAhh summer. No Classes. Baseball. Opera Festivals. Time to focus on research and starting a new book. But, of course, many computer scientists travel the world to various conferences. I went to too many last year and trying to cut down but many great options abound.<br />
<br />
The <a href="http://acm-stoc.org/stoc2017/">STOC 2017 Theory Fest</a>, June 19-23 in Montreal, five days of conference talks, tutorials, invited lectures and so much more. Sanjeev Arora <a href="https://windowsontheory.org/2017/04/27/theoryfest-update/">has the details</a> over at Windows on Theory.<br />
<br />
The ACM celebrates <a href="https://www.acm.org/turing-award-50/conference">50 years of Turing Awards</a> with a special conference June 23-24 in San Francisco. Tim Berners-Lee <a href="https://www.acm.org/media-center/2017/april/turing-award-2016">takes home</a> this year's prize.<br />
<br />
The <a href="http://computationalcomplexity.org/">Computational Complexity Conference</a>, that meeting that shares its domain with this blog, holds its annual get together July 6-9 for the first time in Latvia. Latvia gave us Juris Hartmanis, one of the founders of the field. <a href="http://computationalcomplexity.org/travelAllowance2017.php">Travel grants</a> available for students and "needy researchers", you don't have to be an author to apply.<br />
<br />
<a href="http://math.utu.fi/cie2017/">Computability in Europe</a>, June 12-16 in Turku, Finland. <a href="http://www.sigecom.org/ec17/">Economics and Computation</a>, June 26-30 at MIT. <a href="http://socg2017.smp.uq.edu.au/socg.html">Computational Geometry</a>, July 4-7 in Brisbane. <a href="http://icalp17.mimuw.edu.pl/">ICALP</a>, July 10-14 in Warsaw. <a href="http://cui.unige.ch/tcs/random-approx/2017/index.php">Random/Approx</a>, August 16-18 in Berkeley.<br />
<br />
If I missed your favorite events, well that's why we have comments.Lance Fortnowhttps://plus.google.com/101693130490639305932noreply@blogger.com5