STOC 2012- workshop and honored talks

I went to an enjoyed STOC this year. Today I talk about the workshops and the papers that either won awards or seem to be in the running. I may blog on other things, or expand on these, at a later point.

1. On Saturday there were two workshops, one on Computational Finance by Mike Kearns and one on the Unique Game Conjecture by Subhash Khot and others (sorry- I don't recall who the other speakers were, though they were quite good- in comments tell me and I'll add it. The program says Arora and Charikar, though they didn't speak. I assume they organized it.) (ADDED LATER- CLARIFICATION AND CORRECTION: There was a Comp Finance TUTORIAL that, when
   it was happening, was the only thing happending, and then later there were FOUR WORKSHOPS going on at the
   same time: Computational Sustainability, Algs for Dist and Streaming Data,
   Algs for Memory-Sensitive Computing, and Unique Game Conjecture.)
   
   1. Computational Finance: A distinguished theorist once told me that he is tired of working on problems nobody cares about so he will now work on Computational Finance. He gave a talk that began A Hedge Fund is a set of Boolean Formulas. By contrast Mike Kearns has actually worked with Lehman brothers (Is that why they were not bailed out? Unlikely.) on REAL questions that arise from Finance. The talk gave the needed background on finance and was excellent. One odd thing: I understood the entire thing. I am not bragging- I suspect that everyone who went did. If I was a snobbish pure math guy I would say Since I understood everything it couldn't have been any good. I of course feel the contrary way- it is WONDERFUL that I understood the whole thing. This is partially because he skipped details which is a good thing to skip. Slides are here.
      
   2. Unique Game Conjecture: For past work on this I can't do any better than Lipton's blog here, Khot's surveys and slides here. Khot's talk were a good review if you already knew the material and a good intro if you didn't. The other talks introduced a possible approach to disproving the conjecture. Very High Level View: There is an algorithm using the eight level of the Lasserre hierarchy of SDPs that MAY disprove the UQC. The usual counterexamples don't work. (I may not be stating this quite right.)
      Note that: (1) The community of people who study UGC seems to NOT have a consensu of whether its true or false.
      And those who think its TRUE or FALSE are not dogmatic. (2) It may be resolved before I do my next Poll. If not then I'll
      ask about it. (3) Even if its false it has lead to results of interest that do not assume it.
      
2. There were poster sessions for graduate students. In some ways these are better than talks since you can interact.
   (ADDED LATER- A commenter helpfully pointed out that the posters were NOT just for graduate students.)
   
3. Kasper Green Larsen won best Student Paper award and co-won Best paper award for The cell Probe Complexity of Dynamic Range Counting
   which proved better lower bounds in the cell probe model. The talk inspired me to read the earlier papers on this material.
   
4. Fiorini, Massar, Pokutta, Tiwary, de Wolf co-won best-paper award for Linear vs Semidefinite Extended Formulations: Exponential Separation and Strong Lower Bounds. This paper seems to use Quantum Techniques to solve a classical problem.
   
5. Most of the time there were two tracks so there were two talks going on at the same time. There were five exceptions: the best student paper and the two best papers, and in addition three other papers (the numbers work out that way since the best student paper also co-won best paper award). I assume those three are being unofficially acknowledged as runners-up for best paper or some such (I do NOT have inside information). Those three papers were
   
   1. Julia Chozhoy's Routing in undirected graphs with constant congestion.
      
   2. Chan-Kleinberg-Shmoys Improving Christofides algorithm for the s-t path TSP For the METRIC TSP problem the best known upper bounds is STILL 3/2. WOW. There are some lower bounds (see On Approximation Lower Bounds for Tsp with Bounded Metrics for a list of them) but they are pretty weak-- (1+delta)OPT for some small values of delta. (Someone at the conference told me that better was known, like (4/3)OPT, but I have not been able to find it online- if someone can confirm please leave a comment.) This paper is NOT on the TSP, but on s-t-TSP. They give an upper bound of ((1+\sqrt{5})/2)OPT for this problem, breaking the bound of (5/3)OPT. I don't think any lower bounds are known on this problem. (Note that Euclidean TSP can be approximated arb well by the algorithms of Arora and Mitchell.)
      
   3. Virginia Vassilevska Williams Multiplying Matrices Faster Than Coppersmith-Winograd" has been discussed before in in this blog and also in a blog by Lipton. Virginia did not give the talk since she was close to giving birth (I don't know if she has yet). (Prediction: Ryan and Virginia's kid will prove NP is not in ACC₀ by improving the matrix mult bound. Title of the paper: Improving William's Lower Bound by Improving William's Upper Bound by Williams.)
      

STOC Business Meeting

Last night I ran my last STOC business meeting as SIGACT chair. It was a three-hour affair until the hotel staff kicked us out at midnight. Lots of highlights. I put many of the slides online if you want to see details.

We had a very large turnout for STOC, over 360 participants. Being in New York definitely helped as did posters and workshop sessions. There were 90 accepted papers out of 303 submitted.

There were two best paper winners:

• “Linear vs. Semidefinite Extended Formulations: Exponential Separation and Strong Lower Bounds”  by Samuel Fiorini, Serge Massar, Sebastian Pokutta, Hans Raj Tiwary and Ronald de Wolf
• “The Cell Probe Complexity of Dynamic Range Counting,” by Kasper Green Larsen

Larsen also won the Danny Lewin best student paper award. There were three other papers considered strong enough to merit a single session talk.

Sampath Kannan won the SIGACT Distinguished Service Award for his work promoting theory at the National Science Foundation.

Both the SIGACT Distinguished Service Prize and the Knuth Award will be given annually for now because we have many excellent candidates for both. The Knuth Prize will be given in even years at FOCS and odd years at STOC.

SIGACT elections are still going on. Please vote if you are a SIGACT member and haven't done so.

Skipping ahead (so this doesn't become a three-hour post) FOCS 2012 is at Rutgers, ITCS 2013 in Berkeley, SODA 2013 in New Orleans, STOC 2013 in Palo Alto joint with Complexity and FOCS 2013 (and every two years thereafter) hosted by the new Simons Institute at Berkeley. 

2013 STOC PC chair Joan Feigenbaum described a new multi-tier structure experiment for her program committee. 

Finally László Babai led a discussion on ACM publication policies. More on that in a later post. 

Meetings/Conferences/Workshops/Seminars- whats in a name?

In June 11-14 will be a new workshop: Algorithmic Frontiers.




How many venues do we have for meetings?

1. What the call themselves:
   Meetings (e.g., MATHFEST), Conferences (e.g., STOC), Workshops (Barriers), Seminars (e.g., Dagstuhl), Tutorials, Lunches. More?
   (six options)
   
2. Criteria for getting a paper in: Refereed (e.g., STOC): lightly refereed (I think MATHFEST), unrefereed, talks-by-invite-only (Algorithmic Frontiers, Barriers)
   (four options)
   
3. Participants: Open (most)or by-invite-only (Dagstuhl and Bertinoro) (two options)
   
4. Size: This is more informal. However, CCC is small (100), STOC is larger (around 400), FCRC larger still, and Supercomputing is expecting 11,000. Medical conventions can get around 20,000.
   (five options, though could be more or less depending on your mood.)
   
5. Variety of activities: A venue can have any combination of the following: contributed talks (unrefereed), refereed talks (typical STOC), invited talks, rump sessions,
   tutorials, workshops, short courses. (128 combinations, though in reality only about 5 options actually happen, so I'll take it as 5)
   
6. Length: Number of days can be anything from 1 day to 2 months. However, I don't think all 60 options really exist. I've seen 1,2,3,4,5 days, 1 week, 2 weeks, 1 month, and 2 months. nine options.
   
7. Expense: Either expensive or VERY expensive.
   

So that would be 6x4x2x5x5x9x2. That's a lot! Of course its far far less since, for example, an invite-only gathering can only have invited talks. I would guess its more like 5 types. And some are inconsistent (e.g., STOC sometimes has tutorials and sometimes doesn't).

Algorithmic Frontiers seems to be a 4-day open workshop that has invited talks only. I don't know how big it will be but I would guess between 100 and 200.

Do the gatherings that we go to work? As my Software engineering friend Jim Purtilo often says If you don't know your goals you are not going to achieve them. So, what are the goals? Ultimately to help both us as individuals and us as a community in our research. The hope is we learn things and get inspired to work on problems. And these can be done by the formal talks in the ballroom and informal talks in the hallways. Does this happen? Yes. Is it cost effective (not just money but time)? Debatable, as this and other blogs have debated. Here are my experiences. What are yours?

1. DAGSTUHL SEMINARS. These are specialized one-week long meetings by
   invitation only. The talks need not be on the latest/greatest thing and hence are understandable. (I've been to DAGSTUHL- Complexity 3 times.)
   
2. Bertinoro is similar to Dagstuhl. I've been to the RATLOCC 2011 and
   RATLOCC 2009 which are on Ramsey Theory and Logic. Here there were even more talks
   that were surveys or historical-perhaps because math moves slower than computer science.
   If the talks were on the INTERSECTION Of Ramsey Theory and Logic then it would be too specialized.
   (I've worked in both, but not quite together.)
   As is, its a nice mix.
   But the main point- I understood the talks.
   
3. The Center for Intractability sponsors workshops which anyone can go to
   but the speakers are picked by them. I've been to one of the Barriers workshops and it was very good. The speakers have more time then at conferences,
   which is a plus. The Algorithmic Frontiers workshop seems to be in this model.
   
4. The last few CCC's and STOC's that I've gone to I have enjoyed and gotten stuff out of, but not as much as the smaller venues.
   Partly because the talks are shorter.
   which is a plus. The Algorithmic Frontiers workshop seems to be in this model.
   
5. MATHFEST is nice in that there is a VARIETY Of activities- workshops, seminar, tutorials, invited talks.
   Very large which is both good (that's why they can have all of these things and bad (I never met the same person twice).
   
6. One of my colleagues, Jeff Hollingsworth, is organizing SC12, Supercomputing 2012.
   This will have 11,000 people at it. The program committee has over 100 people
   on it. This seems... large. They seem to have a variety of activities
   so it more like MATHFEST.
   
7. Of course the talks are only part of the reason to go to these things. Even so, for me they are a big reason.
   

What venues to YOU get the most out of? Why or why not?

Gödel Prize

The ACM announced the 2012 Gödel Prize awardees, three seminal papers in algorithmic game theory. The prizes themselves will be presented at ICALP in Warwick in July.

Elias Koutsoupias and Christos H. Papadimitriou: Worst-case equilibria, Computer Science Review, 3(2): 65-69, 2009.

Tim Roughgarden and Éva Tardos: How Bad Is Selfish Routing?, Journal of the ACM, 49(2): 236-259, 2002.

Noam Nisan and Amir Ronen: Algorithmic Mechanism Design, Games and Economic Behavior 35: 166-196, 2001.

The first paper introduced the price of anarchy. The second applied price of anarchy to routing problems. The third applied algorithmic techniques and competitive analysis to auctions.

Congrats to all the winners.

Wall Street Complexity

There is much blame to go around for JPMorgan Chase's two billion dollar loss last week but part of that blame came back to us. In a New York Times web piece, How Moore’s Law Affects Wall St. Trading, Quentin Hardy argues

Faster, cheaper computing makes it possible to create more and better models for calculating cash movements, which can be turned into trading instruments. Areas like leasing, mortgages and project finance have exploded – as has the entire financial derivatives market — thanks to cheap computing...

Soon, it becomes nearly impossible to say what is going on where, and you get events like the 1998 blow-up at Long Term Capital Management, the creation and destruction of the subprime mortgage market in 2008 and perhaps even the “flash crash” in 2010. JPMorgan’s loss seems to be the latest in that series.

I've argued the dangers of reducing computational friction before. But here computational complexity comes in a different way. A derivative is just a function of current and future security prices. But a derivative complex enough can have a behavior that even its creator cannot understand. The Clay Math Institute offers a million dollars to settle "P v NP" but it cost Chase two billion.

So THATS why the 17x17 challenge was so hard. Or maybe not.

On November 30, 2009 I posted the famous 17x17 challenge:

(Paraphrase) Find a 4-coloring of the 17x17 grid that has
no monochromatic rectangles. For $289.00. It was solved in 2012
by Bernd Steinbach and Christian Posthoff (I posted about it
here
and will post their paper when they make it it is public, which should be soon.)
Even though it was solved, it seemed to be a hard problem.

On April 28, 2010 (before the problem was solved)
I wondered WHY it was so hard and posted the following question:

(Paraphrase) Consider the following problem:
Given (N,M,c,f) where f is a partial c-coloring of NxM,
can f be extended to a total c-coloring of NxM (without mono rectangles)?
Is this problem NP-complete?

Kevin Lawler emailed
me a sketch of a proof recently! So YES, it is NP-complete!
I cleaned it up, wrote it up, and put in a few other things, and the paper is
here.
(We will be posting to arXiv after we get comments from this blog.)

1. Does this really show why the 17x17 challenge was hard?
   Not really since the 17x17 challenge is just one instance.
   
2. Does this show that grid coloring problems are hard in general?
   Not really since the case we are really interesting in is where
   f is the empty function. While we do not believe this case is
   easy, we have not ruled this out.
   
3. What can we show about the algorithmic complexity?
   The problem is FPT. For fixed c its in time poly(N,M)+O(c^c4).
   

This is a problem for hardness-of-Ramseyian numbers in general. While it seems as if computing (say) Ramsey Numbers is hard, there is no real proof of this. Related problems have been studied by Marcus Shaefer here.
While this work is very interesting
it is NOT the same as showing that finding Ramsey Numbers is hard.I suspect that to prove such things we need a new framework for
lower bounds.

Paying to Publish

You proved a nice theorem, wrote up the paper and submitted it to a major computer science conference. Your paper was accepted! Congratulations. Now pay up.

An author of every paper accepted at a CS conferences is expected to present that paper at the conference. To do so requires at the least paying the registration fees, travel and lodging to go the the meeting. That can easily run one to three thousand dollars (or more) depending mostly on how far you need to travel.

You can use grant money for these expenses. Some conference offer support to those who need it, particularly students. CS departments will often help out if needed. Sometimes people pay out of their own pockets and, in any case, the funds come from limited pots that could have been used for other purposes.

In the "old days" this was less of a problem. There were only one or two conferences relevant to one's field and you were probably going to those conferences anyway. Now as the field has grown and it has been harder to get your papers published in the strongest conferences, you may find yourself traveling just to give the talk. Even many major conferences don't draw many attendees who don't have papers in the conference.

We haven't seen an outcry of these expenses, say compared to the outcry over the cost of digital library subscriptions. Perhaps we consider attending the conference a "reward" for getting published.

We could just eliminate the conferences and publish the proceedings and post videos of talks, made at the home institutions, saving the field huge amounts of money. Then we could actually choose to attend conferences to meet people in our field instead of just talking at them.

Note: Elchanan Mossel had a similar observation in a comment on a recent post.

Is it well known that we need to redefine well known?

A LONG time (so long ago I was a guest poster, not a co-blogger)
I posted
about how calling things that are on You-Tube rare is odd
since ITS ON YOU-TUBE! ANYONE in the world can look at it!
I now have a Contrasting thought: Can something be
well known if its not easily found on the web?

Last week I
posted
a proof that the intersection of a CFL and a REG lang
is CFL that did not use PDA's. I thought it was NOT new and indeed, the
comments politely gave me the proper reference.
So far, so good. But wait--- some of them called the proof Well Known.
Can a proof be well known if its not on the web?
The notion of a proof being well known has always been problematic
since one wonders what the scope is.

1. Addition
   being commutative is well known but might not
   to my 5-year old niece.
   Someone emailed me that I should take this opp to teach her
   about noncommutative algebras.
   
2. Binary search is well known but might not be known to my (then)
   8 year old great nephew.
   Some said I should use this opp to teach him logarithms.
   
3. Induction is a well known technique but it still puzzles some undergraduates.i
4. The poly vdw theorem
   is well known among mathematically inclined
   high school students in Maryland but
   is not even that well known among combinatorists.
   

The point really is well known to who?. But now with the web we can ask a more focused question: Can you find it easily? The proof I posted was not one that I found on the web. So here is what I want your thoughts on:

1. Should we redefine our definition of
   
2. If I were to make an article out of the three short notes on CFL's
   that I posted about, and submit to Math Archives,
   would that help the problem of what is easy to find
   or would it just clutter up Math Archives making things hard to find.
   (I would of course provide all references and make NO claim to
   originality.)
   
3. Should I post to Wikipedia?
   
4. Will the web ever replace
   asking someone who knows stuff?
   

Microsoft saves the Yahoo NY Researchers

I started working with David Pennock on prediction markets back when we both were at the NEC Research Institute in New Jersey a decade ago. After a major reorganization the dropped basic research from their mission, I went back to academics but David stayed in industry research first at Overture which soon was swallowed up by Yahoo. He ended up at Yahoo Research New York in a small but amazingly strong research lab including machine learning theorist John Langford and social scientist Duncan Watts. But with a new Yahoo CEO and Prabhakar Raghavan and Andrei Broder's departures for Google, it  became clear that the days of Yahoo research were numbered. 

Today Microsoft announced that they are hiring 13 researchers from the Yahoo lab including David, John and Duncan as they start a new Microsoft Research Lab in New York, initially led by Microsoft New England director Jennifer Chayes. Lots of nice coverage from the New York Times, All Things D,  blog posts from Jennifer and John, and a pictorial take from Chris Maase. Not the first time Microsoft has done something like this, Microsoft Research Silicon Valley got its start by hiring several researchers from the old Xerox PARC.

I'm happy the Yahoo researchers found a great home but I also mourn the loss of yet another company abandoning basic research in computer science.

Berkeley Wins the Simons

As reported today in the New York Times, the Simons Foundation has chosen U. C. Berkeley to host the new Simons Institute for the Theory of Computing, a $6,000,000/year center for studying core theoretical computer science and its applications to other disciplines. There will be 70 researchers (faculty, postdocs, grad students) at any given time affiliated with the Institute.

This will be a game changer for CS theory.

Is Moore's Law Good for CS?

Roy Friedman writes a blog post on The Expected End of Moore’s Law is Good News for Computer Science.

For a long time, people got used to being lazy. If computers become twice as fast every 1.5 to 2 years, there is no point in investing much efforts in writing efficient code. If something does not run fast enough, simply wait for the next generation of Intel x86 and everything will be resolved. In particular, CPUs became fast enough that traditional programming languages and efficient data structures and algorithms were being abandoned in favor of high level scripting languages whose most sophisticated data structure is an associative array. Suddenly, every Joe-hoe could become a programmer developing sophisticated Web applications with no effort  – no need for hard earned computer science degrees anymore.

Let's ignore the issue as to whether Moore's law is really coming to an end (Moore's law has had 5-10 years left in it since Gordon Moore developed his law). Friedman misses the bigger point, an end of Moore's law will do great harm to Computer Science.

Friendman's mistake is to assume that people always have the same problems to solve. Suppose computers stopped getting more powerful fifteen years ago. Machine Learning as we know now would not have been possible. Nor would we have the advances in graphics, robotics and virtually every other area of computer science. A good deal of CS systems research goes into making these new machines even more efficient, secure and reliable.

Even in theoretical computer science, the advances in computer technology make our work stand out. As we try to tackled larger problems asymptotic algorithmic techniques start dominating the running time. While we can now brute-force solve NP-complete problems on moderate input sizes, as computer performance improves, so does the thirst for solving even larger challenges and the P versus NP problem becomes a harder monster to slay.

Sure Joe-hoe can wait a year or two for his application to run fast without new coding ideas. While he waits Sam-ham takes advantage of new technologies making Joe-hoe's applications out of date.

Without the increased power of computers, we all become hackers to make our programs run better and that is not computer science.

Hanan Samet wins Kanellakis Prize!

(

1. Symposium on Turing in Princeton in about a month
   
2. UMCP is doing a job search for a lecturer
   
3. New York Area Theory Day
   

) The Paris Kanellakis Theory and Practice Award for 2011 went to Hanan Samet from University of Maryland at College Park. See here for the details. He works on data structures THAT PEOPLE ACTUALLY USE! The Kanellakis price honors Theoretical accomplishments that have had significant and demonstrable effect on the practice of computing. This raises the question: What theory accomplishments are
good candidates for the prize (that have not already won it)?

I left Push Down Automata out of my class and learned some things!

This semester in the Ugrad Course titled Elementary Theory of Computation
(Syllabus: Reg Languages, CFLs, Computability Theory, P and NP) I decided to NOT
teach PDA's. I mentioned them and told the students they were equivalent
to CFG's but nothing more.

This lead to a NEW (to me at least) piece of mathematics!

Proving

X={a^nb^nc^n | n ∈ N}

is NOT a CFL is easy using the pumping theorem.
Consider

Y={w | number of a's, b's and c's in w is the same}

How do you prove Y is not regular?
Why don't you just intersect Y with a^*b^*c^* to get X which
you know is not a CFL? I hear you say.
AH- you need to know that CFL intersect REG is CFL.
If we had the PDA/CFG equivalence then this would be an
easy cross product construction. But now?
SO, we need a proof that CFL intersect REG is CFL
that ONLY uses CFL's. That is, DOES NOT use PDA's.
Here is a proof.
We do not believe it is new but have not been able to find a reference.
If you know a reference please comment.
(NOTE ADDED LATER- The commenters politely provided a reference
and I have put it into the paper.)

Another point of interest: How do you show that REG is a subset of CFL.

1. 
   Normally you would note that DFA's are just PDA's without a stack,
   hence every lang recognized by a DFA can be recognized by a PDA,
   and then use PDA/CFG equivalence. I could not use this.
   
2. 
   You could use the proof that any DFA language is a left-linear grammar
   (left linear only has productions of the form X-->aY)
   and this is nice since, in fact, they are equivalent.
   Here is a proof.
   I ended up not doing this but I will next year
   when I do the course.
   
3. 
   On the midterm I had the following question:
   
   

   Recall that if α is a regular expression then $(α) is the
   set of strings that α generates.
   Recall that if G is a CFG then L(G) is the set of strings generated by G.
   
   Prove the following by induction on the formation of a regular expression:
   For all regular expressions α there exists a Context Free Grammar G
   such that L(α)=L(G).
   You cannot use PDA's (Push Down Automata). (If you do not know what this is,
   do not worry.)

   
   I could only ask this BECAUSE they had not seen PDA's or Left Liner Grammars.
   Of the 40 students about 20 got it right.
   
   
4. 
   One of my students, Justin Kruskal, wondered how to go from a DFA directly to a CFG
   (recall that he had not seen left-linear grammars).
   It is interesting to see what untainted students come up with on their own.
   He came up with a proof
   which is
   here.
   It is a weaker result than the left-linear grammar equivalence, but its his!
   

Questions for YOU, the readers.

1. 
   What do you think of leaving out PDA's? (I may heed your advice
   next spring when I teach it again.)
   
2. 
   Is the proof I point to that CFG intersect REG is CFG, that only uses CFG's, new?
   If not please give a reference. A comment like Bill you idiot, this is a well known proof
   that I have neither a reference nor a website to point to.,
   is not helpful. If you DO have a reference or website to point to you can call me whatever you like.
   
3. 
   Have you ever learned some new math be leaving something OUT of a course?
   

CS in the Sunshine State

As many of you've heard the Dean of Engineering at the University of Florida is planning deep cuts to the Computer and Information Science and Engineering Department (CISE) and focusing its mission solely on teaching. Here is the relevant part of her plan.

Roughly half of the CISE faculty would be offered the opportunity to move to Electrical and Computer Engineering, Biomedical Engineering or Industrial and Systems Engineering.  These faculty would continue to support the graduate and research mission in the Computer Engineering degree track.  The choice of which faculty and which departments will be made based on fit with the research program and with the receiving departments. Staff positions in CISE which are currently supporting research and graduate programs would be eliminated.  The activities currently covered by TAs would be reassigned to faculty and the TA budget for CISE would be eliminated. The faculty remaining in CISE would then focus their efforts on teaching and advising students in the existing Computer Science BS and MS degree programs, offered through both the College of Engineering and the College of Liberal Arts and Sciences.  Their assignments would change to reflect this new educational mission with sole focus on delivering quality education for students in these degree programs.  Any faculty member who wishes to stay in CISE may do so, but with a revised assignment focused on teaching and advising.

In other words Florida is eliminating core Computer Science research, something that makes no sense for a state flagship research university in this day and age. There is a website and petition protesting the move which has caused the Dean to respond. Perhaps because of geographical closeness, this was a big topic of discussion when I was down at Georgia Tech last week. The current and founding Deans of the College of Computing at GT wrote strong letters to the Florida president. The CRA has also expressed their concern.

Certainly the president and dean deserve much of the blame to allow the targeting of computer science at Florida. But as Steven Salzberg of Forbes points out, the real villains lie in Tallahassee with a governor and legislature that has cut funding for the school by 30% over the past six years.

How important is the PROOF of Cooks theorem for my ugrad class?

I am teaching Automata theory this semester. The topics are basically (1) Regular Languages, (2) Context Free Languages, (3) Decidable, undecidable, and c.e. sets, (4) P, NP, NP-completeness.

Other things can be added like Primitive Recursive Functions, the arithmetic hierarchy, the polynomial hierarchy.

I am considering NOT proving Cook's Theorem. State it YES, say how important it is YES, but prove it NO. I am not sure if I want to do this. This post is an attempt to get some intelligent comments on this. My mind is not made up yet so this is I raise the question TRULY non-rhetorically. Some thoughts:

1. The proof is coding a Turing Machine computation into a formula. It is interesting that you can do this. The details of it are not so interesting.
2. The very good students (I would guess 5 out of my 40) will get it. The bad students never get it. I am oversimplifying--- and if this was a reason to not teach a topic I may not have much of a course left.
3. The time spend IN CLASS on this is not so much- one lecture. The time spend in OFFICE HOURS on this re-explaining it is a lot. And its not clear that it helps.
4. Showing them NPC reductions is more important and more interesting. This is what I would put in instead. I usually only get to do a few.
5. Cook's Theorem is SO fundamental that the students should SEE a proof of it even if they don't understand it. but I am not a fan of they should see it even if they don't understand it.
6. Cook's Theorem, like many things, you don't get the first time you see it, but you do the second, helped by having seen it once.
7. Even if we now they mostly won't get it, we want them to know that we WANT them to get it.
8. Students should know that the proof that SAT is NP-complete goes all the way back to the machine model (very few other NP-completeness proofs do). Is it good enough to TELL them this. I would DEFINE Turing Machines, SAY that you CAN code a computation into a formula, but not actually do it?
9. I like to teach things that I can ask problems about. Cook's theorem IS okay for this- I usually show how to make a formula out of some TM instructions and leave as HW making a formula out of other TM instructions. Even so, not that much can be asked about it. The students have a hard time with this (Much more so than other parts of the course) so I wonder if its too much sugar for a cent.
10. I teach this course a lot so I want to mix things up a bit. I realize this is not really a good reason for the students.
11. An argument for: See how it goes! The decision I make this semester need not be what I always do.

Some Announcements

STOC early registration deadline is Thursday. This year STOC will have both tutorials and workshops and its second poster session. Hope to see you all there.

The Simons Foundation is offering Ph.D. Fellowships in Theoretical Computer Science. Deadline May 1.

Finally a big congratulations to Josh Grochow who defended his thesis yesterday at the University of Chicago. Josh was co-advised by Ketan Mulmuley and myself and he'll be joining Toronto as a postdoc next year. Josh is my seventh and last Ph.D. at Chicago.

ACM/IEEE Curriculum 2013

[STOC 2012 Early Registration Deadline Thursday]

On a roughly ten-year cycle, the ACM and IEEE Computer Society get together to create a list of core topics that every getting an undergraduate CS degree should know. The joint task force has a strawman draft proposal and would like your comments for a final report hopefully next year.

This version breaks the requirements into Core-Tier 1 and Tier 2 with the more critical material in Tier 1 and also suggests some elective topics.

In Algorithms and Complexity there is a combined 21 lecture hours of material for Tier 1 and Tier 2 that should comfortably fit into a single quarter long course though that seems aggressive given the list of material. That is built on 41 hours of "Discrete Structures" that includes basic combinatorics and proof techniques. It's a testament to the fundamental importance of theory that it holds more core hours than most other areas.

While I'm always wary of outside committees setting courses and topics, these reports do give guidance in what the "community" believes are important topics for all well-trained computer scientists to know. They can heavily influence curriculum in theoretical computer science especially at the too many CS departments that don't a significant theory group. So take a look at the draft and give your comments to the task force.

Unique Golf Winners

In the Masters Golf Tournament held last weekend there were 55 players who had a final score between 10 under par and 9 above. By the pigeonhole principle one would expect many players to have the same score and in particular multiple players to have the best score. There was a tie for first that required a playoff.

But this is the exception, there were only four playoffs in the last twenty years of the Masters. In most years the Masters tournament has a unique player with the lowest score. Why?

I used Golf Tournaments to motivate the Mulmuley-Vazirani-Vazirani isolation lemma. If you have a collection of sets over {1,...,n} and choose random weights w₁,...,w_n from {1,...,r} let the weight of a set be the sum of the weights of its elements. The MVV lemma states there will be a unique maximum weighted set with probability at least 1-n/r.

It's a cool lemma with a short proof: you argue that with high probability each element i is either in all or none of the max weighted sets.

So how do I tie the lemma to golf tournaments? Actually I don't see a direct connection. But the spirit is the same.

I'll be on that list until the day I die. Or later.

How hard is it to get OFF of lists?

1. Univ of MD at College Park (UMCP) Professor Carl Smith was an editor for JCSS before his death in 2004. I put together a memorial issue of JCSS in his honor that appeared in 2008. SO HOW COME HE IS STILL GETTING ISSUES OF JCSS AT UMCP IN 2012? Normally I would email JCSS about this, but whenever I do that they stop it for a while and then it starts again. So I am not going to bother.
2. I recently got the following email:

   
   William Gasarch
   SIGACT News
   
   Hi William,
   
   The winners of Russia's prestigious Debut Prize are
   presently in the U.S.  The newest of the winning books
   is Irina Bogatryreva's Off The Beaten Track which
   contains her story and two others about hitchhiking in
   Russia.  Irina is also available for interviews as she
   speaks English fluently!
   
   Please let me know if you would like to receive a copy
   of this new and interesting novel.
   
   The Debut Prize winners will be visiting select cities
   (Washington, Boston and New York) during their stay and
   will also return in June for BEA.
   
   I look forward to your thoughts.
   
   Best,
   Shirley
   

Why did I get that? As SIGACT NEWS book review editor I am on lists of book review editor. Technology is sophisticated enough generate lists of book review editors. I suspect it is not cost effective to figure out which editor is appropriate for which types of books since email is free. I have sometimes gotten actual books in the mail that are not math or CS--- that seems like more of a waste of the companies money (though the Biography of Ted Kennedy that I got was a good read.)

Is this a problem? Overall yes since it costs society something (money? time?) to have people (even dead people) on lists where they shouldn't be. But there does not seem to be an incentive on anyone who could fix it to fix it.

Guest post on Tom Cover by Yoav Freund

(Details on registration and student travel awards for the 2012 IEEE Conference on Computational Complexity in Porto available at here.

New York Area Theory Day information here.)



Tom Cover passed away recently. Today we have a guest post about him from Yoav Freund which was written with help from Gabor Lugosi, Nicolo Cesa-Bianchi, Avrim Blum, Rob Schapire, Sanjoy Dasgupta and Manfred Warmuth.

Tom Cover was a leading light, a mentor and an inspiration. I was shocked to hear of his passing away. It was only a few weeks ago that I saw him in the recent ITA conference in San Diego. As usual, engrossed in conversation with a young colleague, gesticulating with his long arms to punctuate his words.

I was first introduced to Cover's work when, as a graduate student in UCSC, I read the classical book of Cover and Thomas on Information theory. Lured by the psychedelic cover I was enchanted by the lucid examples (betting in the horse races) and the elegant math. Like me, many computer scientists were introduced to the deep connections between probability, information, coding and prediction. It is a standard reference for information theory in computer science.

Beyond the book, Cover wrote wrote many of the foundational papers in information theory and its applications. A very partial list of his contribution include his work with Peter Hart on the convergence of the nearest neighbor classifier, His work on the capacity of linear classifiers preceded Vapnik and Chevonenkis. His work on finite memory algorithm for deciding whether the bias of a coin is rational or irrational is a beautiful mind-bender. His papers on gambling and portfolio management started much of the work on online learning.

Speaking of online learning, Cover took part in the first workshop on online learning that was held in UC Santa Cruz at 1992. Cover, with his typical sense of humor, suggested we call the workshop something for nothing. Later we had a bon-fire by the beach, I will always remember Cover as he was that day, a brilliant scientist, a wonderful communicator, a pursuer of beauty and of fun.

Annotated Bibliography

There's also his work on "Nearest neighbor pattern classification" (mid-60s, with Hart).

Yes, that's a very important one. He had two other early influential papers on nearest neighbor classification:

Thomas M. Cover. Rates of Convergence for Nearest Neighbor Procedures. Proceedings of The Hawaii International Conference on System Sciences, Honolulu, Hawaii, January 1968. Thomas M. Cover. Estimation by the Nearest Neighbor Rule. IEEE Transactions on Information Theory, IT-14(1):50--55, January 1968.

Even before Vapnik-Chervonenkis, he calculated the VC shatter coefficient for half spaces:

Thomas M. Cover. Capacity Problems for Linear Machines. Chapter in the book Pattern Recognition, Thompson Book Co., 1968. ed. by L. Kanal.

Then, of course, he was among the pioneers of online learning:



Thomas M. Cover. Universal Gambling Schemes and the Complexity Measures of Kolmogorov and Chaitin. Stanford University Dept. of Statistics Technical Report No. 12, October 1974.

Robert M. Bell and Thomas M. Cover. Competitive Optimality of Logarithmic Investment. Mathematics of Operations Research, 5(2):161--166, May 1980.

Thomas M. Cover. Log Optimal Portfolios. Chapter in Gambling Research: Gambling and Risk Taking, Seventh International Conference, Vol 4: Quantitative Analysis and Gambling, ed. by W.E. Eadington, 1987, Reno, Nevada.

Paul H. Algoet and Thomas M. Cover. Asymptotic Optimality and Asymptotic Equipartition Properties of Log-Optimum Investment. The Annals of Probability,, 16(2): 876-898, 1988.

Robert Bell and Thomas M. Cover. Game-Theoretic Optimal Portfolios. Management Science, 34(6): 724-733, June 1988.

He was among the first to use Blackwell's approachability for online learning:

Thomas M. Cover and David H. Gluss. Empirical Bayes Stock Market Portfolios. Advances in Applied Mathematics, (7):170-181, 1986 This one was a big seminal paper for structural risk minimization: Andrew R. Barron and Thomas M. Cover. Minimum Complexity Density Estimation. IEEE Transactions on Information Theory, 37(4): 1034-1054, July 1991.

Avrim Blum says: I don't know if the following had a big influence on COLT but I remember Ron Rivest describing this result which totally blew my mind: COVER, THOMAS M (1973). On determining the irrationality of the mean of a random variable. Ann. Math. Statist. 1862-871. COVER & HIRSCHLER (1975). A finite memory test of the irrationality of the parameter of a coin. Annals of Statistics, 939-946

You are observing a sequence of flips of a coin of unknown bias p, and after each flip must predict if p is rational or irrational. Shows that with prob 1 you can do this making only a finite number of mistakes....

We Think Like Our Fields

Have lunch with economists and they'll talk about the decision making processes and equilibriums of everything from politics to sports. Computer scientists worry about the misuse of information. Systems people create policies that look like computer programs. Mathematicians internally create models of society and derive consequences from it. I find myself treating the world as one large computational process. Isn't it?

It's not just academics, I've seen the same kind of thinking from lawyers, doctors and business owners. In one sense this isn't a bad thing. It's hard to reason about the world and using our tools and talents to makes sense of it all helps us cope with society. We all have our own religion whether it be spiritual or scientific. 

The problem comes when we just hang with our own, in our social networks both in person and online. We start believing that everyone else thinks the same way we do. Then we have difficulty working with people outside our community and that just isolates us even more. 

Trick question or Stupid question?

April fool days Blogs or Columns may

present an open problem as closed,

present a closed problems as open,

make us wonder if it's a joke or not, (Lance STILL isn't telling!), or

make us question some well held beliefs.

This year I will take a different route- similar to what Lipton did here, which is NOT try to fool you, but present a post ABOUT tricky or foolish or odd things.

When is a trick question a stupid question? I give some examples and my opinions. But I want your opinions- are these questions (with the answers I give) TRICK QUESTIONS or STUPID QUESTIONS?

1. How many states are in the United States? Answers and Commentary
2. What is the least common Birthday in America? Answers and Commentary
3. What is the degree of (x-a)(x-b)(x-c)... (x-z)? Answers and Commentary
4. What US state has the eastern most point in America? Answers and Commentary
5. What is the least common first names for a U.S. President? (The answer is a tie.) Answers and Commentary
6. Which two numbers come at the end of this sequence?

   2,4,6,30,32,34,36,40,42,44,46,50,52,54,56,60,62,64,x,y

   Answers and Commentary. See also this blog entry on the problem.
7. An expert on tracking animals notices one day that there are bear tracks and rabbit tracks converging on the same spot. He can estimate that they converged at 6:00PM with a margin of error of 17 seconds. Hence they must have been there at the same time. He also notices that from the spot they converged only rabbit tracks can be found. HOW CAN A RABBIT EAT A BEAR FOR DINNER? Answers and Commentary
8. There are 6 blue socks, 8 white socks, and 10 black socks in a drawer. How many do you need to take out of the drawer in order to get a pair. Answers and Commentary
9. What is the square root of nine? Give the answer as an anagram of the question. Answers and Commentary

The Value of an Academic Publication

Russell O'Connor's paper was accepted into last years ACM SIGPLAN Workshop on Generic Programming. Russell put the final version of his paper on the ArXiv under a public domain dedication. Russell couldn't transfer author's rights to the ACM since he gave them up. After much discussion the ACM decided not to publish the paper in the proceedings. The abstract in the proceedings states

We note that one of the papers presented in the workshop is not included in the proceedings. This paper, "Functor is to Lens as Applicative is to Biplate: Introducing Multiplate" by Russell O'Connor, is accessible as arXiv:1103.2841v2 [cs.PL].

Russell gives his account but he focuses on ArXiv instead of the public domain aspect. In the STOC CFP we encourage putting your submissions on ArXiv and similar sites. The issue that worried ACM was the loss of rights. ACM could have published the paper, it was in the public domain, but it wouldn't have control of that publication and didn't want to set precedent. Scott Delman of the ACM responded here.

An academic paper you write has little direct value to you (the paper itself not the Intellectual Property within). No one is likely to give you any money for that paper. But your paper does have financial value as part of a collection in a journal or conference proceedings. Commercial and non-profit publishers know how to collect on this value. You might complain that this puts your paper behind a firewall but all the major publishers in CS allow you to post earlier drafts on your homepage and archive sites. As long as you make that effort, people will have access to your papers.

It does take some money (or considerable person hours) to maintain even an electronic journal or conference proceedings. But publishers get more value than that. For the ACM, the DL revenue is a major source of funding for ACM activities and those of the SIGs.

Of course you should never trust the opinion of someone who has a financial interest in a position and as SIGACT chair, we certainly make use of the DL revenue. We are hoarding some in case the DL revenue shrinks in the future.

It seems a shame to leave the monetary value of our papers on the table but also that value shouldn't be exploited. Big discussions will continue on the publications issue, at ACM and other publishers and at all levels of the CS community. There will be a Dagstuhl workshop focused on this topic in the fall. Figuring out the right model for publications will not be an easy one.

My biggest fear is that lack of a plan will lead to a degradation in the quality of our publications and then everyone loses.

Sanjeev Arora wins ACM-Infosys Award

Sanjeev Arora will receive the 2011 ACM-Infosys Foundation Award, the highest honor ACM gives to a mid-career scientist.

Sanjeev Arora is one of the architects of the Probabilistically Checkable Proofs (PCP) theorem, which revolutionized our understanding of complexity and the approximability of NP-hard problems. He helped create new approximation algorithms for fundamental optimization problems such as the Sparsest Cuts problem and the Euclidean Travelling Salesman problem, and contributed to the development of semi-definite programming as a practical algorithmic tool. He has played a pivotal role in some of the deepest and most influential results in theoretical computer science, and continues to inspire colleagues and new generations of researchers.

Congratulations to Sanjeev!

In other news, the IEEE Computer Society W. Wallace McDowell Award is being awarded to Ron Fagin, and the US gives a big push for big data (CCC blog has details).

Another reminder for upcoming deadlines: STOC Posters (3/31), ACM Turing Student Travel (4/2), STOC Student Travel (4/4) and FOCS papers (4/4).

"Math was a mistake- I made it too hard"

(REMINDER- IF you are a STUDENT who wants to GOTO STOC 2012 but needs money to go then you should GOTO the STOC 2012 homepage and click on Travel Support. Deadline to apply: April 4.)

In the movie Oh God Book II God, played by George Burns, says

Math was a mistake, I made it too hard

Or at least I thought he said it. I have repeated this quote both in the blog and as a comment on Scott's blog. As I noted on my blog, if you Google

"Math was a mistake, I made it too hard"

all of the hits that you get lead back to me. This is still true. (Though it won't be after this post goes up.)

I thought it was a great quote so I am surprised it is not better known. FINALLY Oh God Part II came TV so I watched it just to see if what I've been quoting all these years is really in the movie. (Also, its a pretty good movie, for what it is.)

Alas, that is NOT the quote! What God really said was

"Mathematics, that was a mistake. I should have made the whole thing a little easier"

I think my version is better.

There are other misquoted quotes. My favorite: Stalin never said

The capitalists will sell us the rope with which we will hang them.

He did say:

The capitalists will furnish credits which will serve us for the support of the Communist Party in their countries and, by supplying us materials and technical equipment which we lack, will restore our military industry necessary for our future attacks against our supplier. To put it in other words, they will work on the preparations of their own suicide. (The Yale Book of Quotations (2006))

Both for George Burns and Stalin I am troubled- are we better off using the pithy version of the quotes, which DOES capture what they meant, or the original?

We have a similar issue when we teach- do we teach math the way it was invented or discovered (messy but motivated) or the way it is understood now (clean but unmotivated). Hopefully its not an either-or question and we can do some of both.

What is an Elegant Proof?

What is an elegant proof? I do not know and I doubt it can be well defined; however, we all know it when we see it. I welcome comments on the topic; however, I will give a very simple example for a contrast of elegant and non-elegant. All of the math discussed here informally is done formally here.

Consider the following theorem:

There is no 2-digits number that is the sum of the squares of its digits.

One crude measure of elegance is to minimize the number of numbers that you need to check directly are not the sum of the squares of their digits. With this in mind. With this in mind, here are several proof sketches.

1. One could proof this by enumerating all possible 2-digit numbers. If you wrote a program for this then you could use it on similar problems. Even so, I suspect most of us would call this proof NOT ELEGANT. This requires 89 CHECKS.
2. There is a proof that first easily eliminates 10, 20, 30, 40, 50, 60, 70, 80, 90 and then looks at every interval [11,19], [21,29], ..., [91,99]. More elegant than enumeration and certainly shorter. This required 8 CHECKS.
3. There is a proof that looks at the equation 10a + b = a² + b². We look at it mod 2, mod 4, and mod 10. This gives what I thought was the most elegant proof; however, after writing it down carefully it was about the same length as the interval proof. This required 2 CHECKS.

Consider the following theorem:

There is no x ≥ 2 that is the sum of the squares of its digits.

The cases of 2 ≤ x ≤ 9 and x ≥ 100 can be done with zero checks, so using the best proof of the last theorem, we can do this theorem with 2 checks.

Consider the following theorem.

The only 3-digits number that is the sum of the cubes of its digits is 153. (NOTE ADDED LATER: This is INCORRECT. A commenter pointed out that 370, 371, 407 also work. I will fix the proof and statement later and see if these are the only ones. Score a point for the `do it by a computer enumeration' argument!)

I have a proof of this which is... not quite elegant but not brute force. I get it down to only 21 CHECKS. If you have a better proof in terms of NUMBER OF CHECKS that is not contrived to reduce NUMBER OF CHECKS I would be very interested to see it. Of course, I cannot define contrived rigorously or elegantly.

David Waltz (1943-2012)

David Waltz, head of the Center for Computational Learning Systems at Columbia, passed away yesterday after a battle with a brain tumor at the age of 68.

David Waltz is best known for his research in artificial intelligence but I'll remember him most for his leadership of the NEC Research Institute when I was there. David fought hard and risked his career to protect basic research, particularly theory, at NEC. He would end up losing the presidency of NEC in this conflict. It is a great leader that is willing to risk all to support his people.

A Busy Time of The Year

It's spring break week at Northwestern so life is supposed to be quiet. No such luck.

Endre Szemerédi will receive the 2012 Abel Prize, perhaps the most prestigious annual award in mathematics. Tim Gowers has a nice summary of his work.

With this tweet the head of Yahoo Research officially leaves for Google.

Farewell @YahooLabs it was a fantastic ride. Hello @google
— prabhakar raghavan (@WittedNote) March 20, 2012

This likely marks the beginning of the end for what was a great corporate research environment.

FOCS submission deadline is April 4. There are some minor changes in the submission format from last year.

Registration for the ACM Turing Centenary Event is full but students can still attend through a limited number of ACM SIGACT Student Scholarships.


Registration for STOC is now live. The final program will be posted soon.

• Submit to STOC's second poster session. Deadline March 31.
• Student Travel grants are available Deadline April 4
• This STOC will have the inaugural Student Presentation Award

Even as I write this post, breaking news that U. Illinois president Michael Hogan resigned. Can't wait to see what Jeff has to say about this.

Heading South

Starting in July, I'll be chair of the School of Computer Science in the College of Computing at Georgia Tech. Annie Antón from NC State will chair the School of Interactive Computing. Here's the official announcement. I'm truly excited to be working with Annie, the Dean of Computing Zvi Galil and the incredible faculty there to move Georgia Tech forward.

I can anticipate many of your questions: How does moving from the land of Lincoln to the land of Lipton affect the blog? How do I get a job at Georgia Tech? Wait, does this mean there is a theory opening at Northwestern? Is this really the fourth job you've had since starting the blog ten years ago? All in due time.

Intel Science Talent Search

Last week I went to the Intel Science Talent Search Awards Ceremony in DC, probably the most prestigious math and science competition for American high school students.

I mentored one of the finalists, Adam Kalinich, of the Illinois Math and Science Academy. Adam studied poset games, where each player takes turns picking an element x of a finite poset and removes all y ≥ x. First one to empty the poset wins. The complexity of deciding who wins a poset game is wide open. Adam showed how to convert a game where one players wins to a game where the other wins, a surprisingly tricky task. His paper appeared in IPL (also on ArXiv).

Lots of math and computer science among the finalists and winners. The other Illinois finalist, Jordan Cutler, worked on practical implementations of quantum cryptography with Prem Kumar, another professor in my department. Jordan, who is a cousin of complexity theorist Steve Homer, came in 10th place.

Anirudh Prabhu had the coolest math result on perfect numbers. It's been conjectured that there are no odd perfect numbers. Anirudh showed a non-constant lower bound for odd perfect numbers (if they exist) as a function of the number of factors. Only constant lower bounds were known before. Anirudh came in 7th place.

David Ding got 4th place for his work on representation theory of Cherednik algebras. I don't know what those are either.

First place went to Nitin Tumma for work related to cancer.

The ceremony itself was a great scene. I'm a sucker for the pomp and circumstance. Walter Isaacson gave the keynote address and we all got autographed copies of his biography of Steve Jobs. Great fun was had by all.

I've seen the future of American science and it is awesome.

Judea Pearl wins Turing Award

(In this age of lightenting fast communication I suspect you all already know that Judea Pearl won the Turing Award. Even so, it is worth posting about.)

Judea Pearl has won the 2011 Turing award (given in 2012). (see here for the announcement). He is not a theorist; however, he did champion the use of probability and graph theory in AI.

Strong AI is the attempt to make computers match or exceed human intelligence. People in Strong AI might see how humans do things and try to get a program to mimic that. Putting aside philosophy (are we all just rather complicated DFA's?) the goal of Strong AI seems to just be hard to do even if it is possible (complexity issues?)

Weak AI has more modest goals (and a much shorter Wikipedia Page)- lets get a computer that can do a well defined task (e.g., Medical Diagnosis) well. They want to get things to work and may very well NOT take how humans do it as an inspiration. Do humans do the kinds of probabilistic calculations that Judea Pearl works with? I tend to doubt it.

Once Strong AI produces real results it is called Weak AI. Once Weak AI produces real world products its called something else (Robotics, Nat. Lang Proc, Vision, there are other examples).

I ask all of the following nonrhetorically. NONE of the questions are meant to question the award.

Did Judea Pearl work in Strong AI to Weak AI?

Was Judea Pearl one of the first people to incorporate serious AI on a more rigorous foundation?

Does AI use serious math? (I know that Control theory does, though is that AI?)

Did Judea Pearl (or his group) build software that is actually being used someplace?

What is the criteria for good work in AI?

Who might be the next AI Turing Award Winner?

How do legit fields of knowledge decide between competing theories? How does Astrology?

Euler was born April 15, 1707. Hence by the Western Astrology that we all ignore he is an Aries. However, I recently heard about another way (also worth ignoring) of doing the signs where he is a Pisces (see here). The other system has 13 signs. (There are some other systems, all worth ignoring, here.) For a serious article about what astrology really claims to say and why its worth ignoring see here.

What does a field of study do if there are several competing theories?

1. The Natural Sciences: I would like to think that the truth wins out... eventually. There may be struggles and politics and whatnot but in the very end experiments are performed and the more predictive theory wins out (I know its more complicated then that.) There are some fields where it is hard to do experiments (e.g., String Theory). Others where the theory gives great explanatory power but might be hard to do direct experiments (Evolution). Those cases may be hard to deal with, but they manage. Does String Theory have great explanatory power?
2. Mathematics: Here the question is not WHAT IS TRUE since we can use proofs (Again, I know its more complicated than that) but WHAT IS WORTH STUDYING. Applied Math may still use the real world for a litmus test to some extend. More abstract kinds of math may be harder to test by looking at the real world. Do Large Cardinals exist? Is the Axiom of Determinacy true? Some people claim that they look for internal consistency and also intuitions. And some people live-and-let-live (you want to use AC, fine, I won't) (Again, I know its more complicated than that.)
3. Astrology : What does a field do when its predictions are either vague or no better than chance? If there was a well designed experiment to test which theory has more predicative value then I suspect they would all be found wanting. (Then again, I'm a Sagittarius and we are known to be skeptical.) So what other criteria could they use? Internal Consistency and Intuition? Whichever one makes people feel better (some astrologers might claim that they are really psychologists, telling people what they want to hear to sooth them). Whichever sells more books? Makes more money? Is there some sort of aesthetics involved? I ask this nonrhetorically. (An idea for a scam: The old astrology doesn't work because they don't take into account relativistic effects on the planets. Use my Relativistic Astrology! For people who like what they believe in to have some buzz words from science thrown in!)

This does raise the general question- if there are competing theories in a field where its hard or impossible to do experiments, what does a field do? Whoever yells loudest wins?

March Madness

Once again, America's favorite binary tree, the NCAA Men's National Championship Bracket. The tree seems to get more unbalanced every year. There are four regions, the East has the traditional 16 teams, the West and South have 18 teams each and the Midwest has 19 teams for a total of 68 teams. Single elimination starts tomorrow.

Many Americans participate in office pools where they fill out the bracket to predict which team wins each game. There's lots of math one can use for your bracket. But here is my advice: Pick the higher seeded teams to beat the lower seeded teams. Every time. There will be upsets but you can't predict where they will be so you have the best chances predicting none of them.

The most likely seeds to make the final four are two number 1's, a number 2 and a number 3, 3 times in the last 27 years. So why follow my advice which predicts four number 1's. Because there are 12 ways to get 11 2 3 and only one way to get 1 1 1 1 and you have to pick a specific combination when you fill out your bracket. The four first seeds all went to the final four only once in the last 27 years but given there's only one such combination that makes it more likely than any other possibility. 

May the madness begin.

Scott wins the Waterman

The NSF's most prestigious prize, the Alan T. Waterman award, recognizes an outstanding young scientist (35 or under) in any field of science or engineering. Breaking with tradition this year the NSF picked not one but two winners, computer scientists Scott Aaronson (MIT) and Robert Wood (Harvard).

Most of you readers know Scott well. He's already an established leader in quantum computing and computational complexity and has his own awesome blog. Not sure why NSF decided to use a photo of Scott proving Karp-Lipton wearing a skirt. The CCC blog post points to Scott's TedxCaltech talk. I'll just link to the podcast I had with Scott back in 2005.

Computational complexity has won two Watermans in the last three years as Subhash Khot received the award in 2010.

Robert Wood is the principal investigator of the RoboBees project, which is pretty much as the title suggests, insect-inspired robots. Sweet revenge for being called the number one example of government waste by Sean Hannity.

When a+b is harder than b+a

Is 1+4 a harder calculation than 4+1? It may be if you are 2+3 years old. I asked my 7-2 year old great niece Noelle the following sequence of questions. I include how long it took her to answer.

Bill: How old are you?

Noelle: (2 seconds) 5

Bill: What is 3+2

Noelle: (3 seconds) 5

Bill: What is 2+3

Noelle: (2 seconds) 5

Bill: What is 4+1

Noelle: (1 seconds) 5

Bill: What is 1+4

Noelle: (8 seconds) 5

Bill: What is 7 take away 2

Noelle: (4 seconds) 5

Bill: What is the least d such that there is general dth-degree equation.

Noelle: (11 years) 5

Bill: What is the least k such that the kth Ramsey Number is not known

Noelle: (21 years) 5

The most interesting of these to me was that 1+4 took much longer than 4+1. Why is this? To do 1+4 she starts at 1 and adds 1 to it four times so its 1 + 1+ 1+ 1+ 1. To do 4+1 she starts with 4 and adds 1 once, 4+1. More generally, if we don't use the addition is commutative and we view +1 our basic operation than the complexity of a+b is b.

It is important to realize that concepts such as commutativity of addition which are now obvious to us as adults, there was a time when it was not obvious. Or perhaps not obviously useful for calculations.

Could a model of children's addition be defined and studied? Would this be a Math Project, a Math Ed Project, or a Child-Development Project? Has it already been done? I suspect that how children learn things has been studying extensively, but that well defined questions of complexity-of-children's-addition has not. My ONE data point suggests that the complexity of a+b is b, but to really study this you would of course need more samples. SO, if any of you relatives that are 5 or under (but can talk), and try this out, let me know what you find.

The Internet of the Present

On this blog we rarely get non-spam comments on posts more than a few days old. Sometimes I can bring up a topic I had posted on just a few months ago and no one will notice. When people said they enjoyed my blog I used to ask them what posts they liked. I would just get a blank stare. I don't ask anymore.

In theory you can look at our old posts through the "Blog Archive" section on the left column (if you are reading this on the blog website). I doubt anyone actually does. Occasionally people get to old posts via Google searches but I've come to the realization that most posts I wrote more than a few weeks ago will never be read again.

That's too bad. Many of them are still quite relevant. But we live in the present. I'm just as guilty as everyone else. Sometimes I'll discover a great new blog and subscribe to its posts. But I'll never go back and read the old posts.

Blogs seem to be going out of style. Twitter don't even try, one cannot easily see someone's old tweets, and any brilliant tweet I make will expire in usefulness in a just a few hours. Google+ is similar. Interestingly Facebook with their new Timeline makes it possible to explore someone's early posts. The past remains there just in case someone cares.

I have no great insights or solutions to this problem. But what does it matter. A week from now you'll forget this post even existed. 

Turing's Titanic Machine!

In the March CACM, Barry Cooper writes

We quote Peter J. Denning introducing the ACM Ubiquity Symposium on "What is Computation?" as saying: "Researchers in biology and physics have claimed the discovery of natural computational processes that have nothing to do with computers."

With Lance Fortnow distinctly underwhelmed: "Some people outside of computer science might think that there is a serious debate about the nature of computation. There isn't."

As often happens when experts disagree, the truth lies somewhere in between.

No it doesn't. My extreme point of view: A strong belief in the Church-Turing thesis that Turing machine captures the true notion of computation now and forever.

What's next? Casting doubt on 1+1=2? Sure no one has yet proved 1+1=3 but that doesn't mean it won't happen someday.

The Erdos- de Bruijn theorem

The mathematician Nicolaas Govert de Bruijn passed away on Feb 17, 2012. The number of things named after him is quite large. I will discuss the Erdos-de Bruijn theorem.

Erdos-de Bruijn theorem: An (infinite) graph G is k-colorable iff every finite subgraph is k-colorable.

I will sketch the proof for the case where G is countable. We can assume the vertices are {1,2,3,...}. Let COL_i be a k-coloring of G restricted to {1,...,i}. We will use the COL_i's to obtain a k-coloring of the entire graph G. We can assume the COL_i's use colors {1,...,k} so we can speak of the least color j such that blah blah.

We color node 1 by the least color that an infinite number of the COL_i's color 1. Then REMOVE all of the COL_i's that do not use that color on 1. (We kill all those that disagree with us! as I told my students.) Note that there are still an infinite number of COL_i's left.

We color node 2 by the least color that an infinite number of the COL_i's THAT ARE LEFT color 2. Then REMOVE all of the COL_i's that do not use that color on 2. Note that there are still an infinite number of COL_i's left.

And so on.

End of Sketch of Proof.

1. This type of argument can be used to proof the following:
   1. If we already have the infinite Ramsey Theorem on N, we can obtain the finite Ramsey Theorem and (with a small trick) the Large Ramsey Theorem.
   2. If we already have the finite dilworth theorem (any FINITE partial order of width w can be covered with w chains) then we can obtain the infinite version of Dilworth's theorem: if an INFINITE partial order has width w can be covered with w chains.
2. The method is called compactness argument and is very general. It is related to topological compactness, but I won't to into that here. (If a reader has a short explanation or pointer, please post.)
3. The method is noneffective in that if you are given a Turing machine that tells you, for all i,j, COL_i(j), then the proof does not appear to be able to give you a Turing machine for a coloring of G. There are two ways this has been formalized, though I list three since the third one strengthens the second one. (For details see my survey of recursive combinatorics here.)
   1. (Bean, 1976) There is a computable graph (Vertex set N, Edge set decidable) that is 3-colorable but there is no computable finite coloring whatsoever. (He also made the graph planar, which was not needed but nice.)
   2. (Carstens and Pappinghaus, 1983) For every k ≥ 3 There is a highly computable graph (Vertex set N, the function that, given a graph, outputs its finite set of neighbors is computable) that is k-colorable but not computably k-colorable. (NOTE: if a highly comp. graph is k-col then IT IS computably 2k-1 colorable.)
   3. (Schmerl, 1980) For every k ≥3 There is a highly computable graph (Vertex set N, the function that, given a graph, outputs its finite set of neighbors is computable) that is k-colorable but not computably (2k-2)-colorable.

Nash and the NSA

By now most of you have heard about Nash's recently released letters to the NSA (press release, letters). Not only did John Nash think about computation and cryptography, there are many ideas in these letters that were a bit ahead of their time when Nash sent these letters in 1955.

• Expressing a cryptographic process as a Boolean function with input bits. 
• Breaking the cryptographic system as a function of the key length.
• Exponential in key length as computationally hard and polynomial in key length is computationally easy.

His conjecture is quite striking.

For almost all sufficiently complex types of enciphering, especially where the instruction given by different portions of the key interact complexly with each other in the determination of their ultimate effects on the enciphering, the key computation length increases exponentially with the length of the key, or in other words, with the information content of the key.

The significance of this general conjecture, assuming its truth, is easy to see. It means that it is quite feasible to design ciphers that are effectively unbreakable. As ciphers become more sophisticated the game of cipher breaking by skilled teams, etc. should become a thing of the past.

The nature of this conjecture is such that I cannot prove it, even for a special type of cipher. Nor do I expect it to be proven. 

Nash's conjecture, even for a specific cipher, would imply P ≠ NP, 16 years before Cook defined the problem, and the significance resonates with the Diffie-Hellman article written 21 years later

Theoretical developments in information theory and computer science show promise of providing provable secure cryptosystems, changing this ancient art into a science.

Given Nash's insights, why did the NSA react so cautiously to these letters.

• This was not a letter from Nobel Laureate Nash but from Assistant Professor Nash.
• There is a strong positive correlation between people who claim they are not a crank and those that are.
• Nash's arguments didn't apply that well to the relatively slow digital computers of the time.
• Nash didn't give a particularly useful cryptosystem.
• I don't even believe Nash's conjecture: There are plenty of complex enciphering techniques, such as the Engima machine, which the NSA did know how to break. Hard to break cryptosystems come from more structured ciphers based on algebraic properties like AES and RSA.

Is 99.8% Secure Secure?

Guest post by Janos Simon

A group of researchers (Arjen Lenstra and collaborators  from EPFL Lausanne and James Hughes from Palo Alto) published a study, Ron was wrong Whit is right, of new vulnerabilities of cryptosystems. The New York Times picked up the story. Although Lenstra et al discuss several cryptosystems, their results are particularly relevant to those based on RSA. The title mirrors their conviction that cryptosystems based on a single random element have fewer key generation problems than RSA, that uses two random primes.

The technical problem they identify in RSA is the following: The RSA cryptosystem uses a modulus n that is the product of two large "random" primes p and q. Actual keys may not be truly random, and this may cause several possible problems:

1. Different users may end up with the same n. Since a user knows the factors p, q, she will be able to decrypt the data of any user with the same modulus.

2. If two users share one of the factors, (user A's modulus is pq, user B's is pr) they will be able to decrypt each other's data. Given two moduli, one can use the Euclidean algorithm to determine whether they have a common factor, and find it if it exists.

Note that the second vulnerability is more insidious: in the first only the user with the matching key can decrypt the messages of its mate, while anyone can  explore the web looking for pairs of keys with a common factor.

The lack of randomness in key generation may be caused by bad choices for the seed of a random number generator. As an extreme example, devices may be shipped with a standard common seed. In this case all devices would generate the same n. In general, if the collection of seeds is a low entropy set, with high probability insecure keys will be generated.

The EPFL group collected 11.7 million public keys "while avoiding activities that our  system administrators may have frowned upon" and essentially found that about 99.8% of the keys were not insecure (to the extent that they did not suffer from the vulnerabilities above.)

Is this secure enough?

Note that .2 percent of 11 million is tens of thousands of bad keys.

To make matters murkier, another group with researchers from the University of Michigan and UCSD did a somewhat similar experiment. Their results are not published yet, but one of the authors, Nadia Heninger blogs about their results in Freedom to Tinker. They find a similar proprtion of bad keys, but they claim that the vulnerability mostly occurs with embedded devices like firewalls and routers, so "important" keys like bank certificates are not affected. Lenstra et al disagree.

Perhaps we should be happy that these vulnerabilities are not due to weak Theory, but to bad implementations of good theoretical ideas....

The Envelope Please

The conference that shares its namesake with this blog has announced their accepted papers. The 27th Conference on Computational Complexity itself will be held in Porto, Portugal June 26-29. If you go, stop by England on the way and celebrate the 100th anniversary of Turing's birth (June 23) in either Cambridge or Manchester.

Lots of great papers accepted to the conference. For biased reasons I like Limits on Alternation-Trading Proofs for Time-Space Lower Bounds by Sam Buss and Ryan Williams. They give some compelling logical reasons why we've hit the limit of current techniques in proving time-space tradeoffs for Satisfiability. Alon, Shpilka and Umans found connections between Sunflowers and Matrix Mulitplication. Finally a plug for my student Josh Grochow's first Complexity paper Matrix Lie Algebra Isomorphism.

Presidents Day Poll- what does the youth of american think about....

(In honor of President's day which was two days ago.)

On Presidents Day last year I had my classes fill out a form saying who they thought was the best, second best, third best, and worst president. I gave them a list and asked them to just mark 1,2,3 (for best, second best, third best) , BAD (for worst) on it. I omitted Obama, Bush Jr, Clinton from the list since they are too recent. So, what does the youth of America think? Or at least the youth taking Honors Discrete Math or Automata theory?

Here is the list or presidents ranked by roughly how well they did. (Some are not included since they did not get any voters pos or neg.) I (somewhat arbitrarily) gave 3 points for each ONE, 2 points for each TWO, 1 point for each THREE and -3 points for each BAD. Are these the best weights to use? Is there a way of arguing which weights are best? This is a variant of a standard voting problem. The standard problem does not include the option of BAD for negative points. I don't think there is an optimal answer. Weights that would NOT be good to use would make the ONES's get a lot more than the TWO's since I suspect this gap was not so large in peoples minds. Or I could have had THEM give point values between (say) 1 to 100 for the ONE, TWO, THREE and between -1 and -100 for the BAD. Maybe I'll do that next year.

1. Abraham Lincoln: 15 ones, 10 twos, 10 threes: 75 points.
2. Theodore Roosevelt: 8 ones, 8 twos, 4 three: 44 points.
3. Franklin D. Roosevelt: 11 ones, 7 twos, 7 threes, one B: 51 points.
4. George Washington: 7 ones, 4 twos, 8 threes, one B: 34 points.
5. Thomas Jefferson: 6 ones, 5 twos, 5 threes: 33 points
6. Dwight Eisenhower: 1 one, 3 twos, 5 threes: 14 points.
7. John F Kennedy: 2 ones, 5 twos, 6 ones, 1 B: 14 points.
8. Woodrow Wilson: 1 one, 1 two, 3 threes: 10 points.
9. Harry S Truman: 2 twos. 6 points.
10. James Polk: 1 one, 1 two: 5 points.
11. John Adams: one 1, one 2, one B: 4 points.
12. William Henry Harrison: one 1: 3 points.
13. Lyndon B. Johnson: one 2, one 3, one B: 2 points.
14. Andrew Jackson: 2 ones, 1 two, 2 B's: 2 points.
15. Ulysses S. Grant: 1 two, 2 B's: -4 points.
16. Zachery Taylor, Rutherford B Hayes, Chester Arthur, Millard Fillmore, Warren Harding, Gerald Ford: 1 B: -3 points.
17. Jimmy Carter: 1 one, 1 two, 4 B's: -5 points. CORRECTION ADDED LATER: SHOULD BE -7. ARITHMETIC MISTAKE. MAKES HIM RANK BELOW BUCHANAN AND TAFT!
18. James Buchanan, William Taft: 2 B's: -6 points.
19. Ronald Reagan: 1 one, 3 twos, one 3, 8 B's: -12 points. CORRECTOIN ADDED LATER: SHOULD BE -14. ARITHMETIC MISTAKE. RELATIVE ORDER UNCHANGED.
20. Herbert Hoover: 5 B's: -15 points.
21. George Bush: 6 B's: -18 points.
22. Richard Nixon: 1 one, 1 two, 10 B's: -25 points.

My thoughts

1. I thought George Washington would do better.
2. I'm surprised that Theodore Roosevelt did so well. Bart Simpsons likes him, though Lisa Simpson prefers FDR (From the episode Bart stops and smells the Roosevelt's.
3. The person who ranked Hayes as the worst president of all time either knows much more about the Hayes administration then I do or was just putting things down at random.
4. The vote for William Henry Harrison was a joke- the guy who voted for WHH is named Henry and liked that his first name was WHH's middle name.
5. Dwight Eisenhower did better than I thought he would.
6. Richard Nixon did worse than I thought he would. I thought today's youth didn't know about Watergate. George McGovern (who Nixon beat in 1972 and is still alive) recently said that if he had won in 1972 then Nixon's legacy would be much better (going to China, Detente with Russia, EPA, Okay on Civil Rights.) Nixon would be considered a left wing democrat today.
7. George Bush did so bad that I think people may have confused him with his son W.
8. Some of my opinion: (1) I rank George Washington first since the very act of STEPPING DOWN after two terms set the tone for peaceful transitions of power. Note that young democracies today the most important election is the one where the person in power has to voluntarily step down. (2) For worst prez I wouldn't call someone BAD just because I happen to disagree with their policies. It has to be someone who (in contrast to Washington) did things that undermine our democracy. Two that come to mind are Nixon (Watergate) and John Adams. (Alien and Sedition Acts). George W Bush (Patriot Act) might also qualify but its too early to tell. Other wartime restrictions on freedom (happened in many wars) might also qualify. The corruption of the Grant and Harding's administration were deplorable but I don't think they rise to the level of undermining our democracy. There are probably other presidents who qualify for this honor but not being an expert on Presidents, I don't know who they are.
9. In the book Hail to the Chiefs (a humorous though mostly accurate look at the presidents) in the first edition she said that Buchanan and Andrew Johnson were not looked upon kindly by historians, which is true. In the second edition she made the points many times with many presidents (including those two) that how well you do is VERY MUCH a matter of timing, luck, and History. To paraphrase Buchanan couldn't stop the Civil War. By that point nobody could. Andrew Johnson had to reunite the country and deal with the South after the Civil War. That's pretty hard too. I agree that there are many thing outside a presidents control, and they some blame or praise may be unwarranted.

Aggie for a Day

About 25 years ago I visited a college friend, David Jackson, then a grad student at Texas A&M. He was a Ph.D. student in Food Science doing his doctorate research on starch. He had a tortilla maker in his lab. Made me wonder if I was in the right field. David is now making tortillas in Nebraska.

Last week I made my second trip to College Station this time to visit the CS department, give a talk and meet lots of great researchers.

Landlocked Texas A&M has one of the world's leading Nautical Archaeology programs. We went to visit and a grad student came out, said "Howdy", and gave us a tour of models of the ships they have been excavating.

Robin Murphy arranged a tour for me at Disaster City (that's us pictured above). Disaster City is one of the largest training grounds for emergency responders with collapsed buildings, rubble piles, derailed trains and other sites to train people, dogs and robots, the last of which is Robin's specialty. Some of Robin's students were testing out a flying video drone that day. Robin gets involved in disaster areas such as Fukishima. Saving lives with computer science. Makes me wonder if I got in the right field.