Go Sox!

Saturday Evening, October 25, 1986: I huddled with about a dozen of my fellow MIT graduate students (and a couple of faculty) watching game six of the baseball World Series in a Toronto hotel room right before the start of FOCS. The Boston Red Sox led by two runs with two out and none on in the bottom of the tenth against the New York Mets. One more out and the Sox would win their first championship since 1986.

The Red Sox didn't win the series that year and failed to return until this year. After an amazing comeback against their rivals, the New York Yankees, the Red Sox will host the first game of the World Series on Saturday against the St. Louis Cardinals.

By far baseball is the favorite team sport among American computer scientists (at least of those that care about sports at all). Why? Mabye because it's a discrete game with a small state space. At Fenway Park (Boston's home field) they use lights to give the number of ball, strikes and outs in unary notation. The game has many nice mathematical properties and not just the myriad of statistics. For example, it is a theorem of baseball that at any point in a half inning the number of batters is equal to the sum of the number of outs, the number of runs scored and the number of men on base. Proof by induction.

The real reasons I love baseball are less tangible. Both a team sport and a one-on-one contest between pitcher and batter. A strategic game dealing with balancing probabilities. Suspense on every pitch. And much more.

By far the plurality of baseball fans in our field seem to root for the Red Sox. Probably because most of us spent at least part of our academic career in the Boston area and Boston takes its baseball far more seriously than any other city. In full disclosure, my favorite team is the Chicago White Sox but I root for the Red Sox in their absence.

Nothing beats attending baseball game live, especially in Fenway. Alas I never managed to attend a world series game though I've come very close.

October 14, 1992: The Pittsburgh Pirates won the National League East and the World Series was scheduled to open during FOCS in Pittsburgh. I wrote for and got tickets to the first game if Pittsburgh made the series. In the NLCS Atlanta scored three runs in the bottom of the ninth of game 7, meaning Atlanta and not Pittsburg would host the series. When Cabrera hit the single scoring those final two runs, I sat staring at the TV and cried.

Conversations with Bill

A guest post from William Gasarch

Why is it hard for us to explain to the layperson what we do? The following true story is telling. I will label the characters MOM and BILL.

MOM: What kind of thing do you work on?

BILL: (thinking: got to give an easy example)
Lets say you have n, er 1000 numbers. You want to find the — (cut off)

MOM: Where did they come from?

BILL: Oh. Lets say you have 50 numbers, the populations of all of the states of America, and you want to find — (cut off)

MOM: Did you include the District of Columbia?

BILL: No.

MOM: Why not?

BILL: Because its not a state. But for the example it doesn't matter because — (cut off)

MOM: But they should be a state. They have been oppressed to long and if they had their own state then — (cut off)

BILL: But none of that is relevant to the problem of finding the Max of a set of numbers.

MOM: But the problem of Statehood for DC is a more important problem.

BILL: Okay, lets say you have 51 numbers, the populations of the 50 states and the District of Columbia.

MOM: What about Guam?

BILL: I should have majored in Government and Politics…

To the person on the street the very definition of a problem is … problematic. Abstraction that we do without blinking an eye requires a conceptual leap that is hard or at least unfamiliar to most people.

Even people IN computer science may have a hard time understand what we are talking about. Here is another real life story between two characters who I will call BILL and DARLING. DARLING has a Masters Degree in computer Science with an emphasis on Software Engineering.

DARLING: Bill, can you give me an example of a set that is provably NOT in P.

BILL: Well, I could say HALT but you want a computable set, right?

DARLING: Right.

BILL: And I could say that I could construct such sets by diagonalization, but you want a natural set, right?

DARLING: Right.

BILL: And I could say that the set of true statements in the language WS1S, but you want a natural set.

DARLING: What is WS1S?

BILL: Weak Monadic Second order with one successor, but I think you agree that if you don't know what it is then it's not natural.

DARLING: Right. So, is there some set that is natural and decidable that is provably not in P?

BILL: AH, yes, the set of regular expressions with squaring that equal Σ^* is EXPSPACE complete and hence provably not in P.

DARLING: Why is that problem natural?

BILL: Good Question! A problem is natural if it was being worked on before someone classified it.

DARLING: Okay. What is the first paper this problem appeared in?

BILL: It was in THE EQUIVALENCE PROBLEM FOR REGULAR EXPRESSIONS WITH SQUARING REQUIRES EXPONENTIAL SPACE by Meyer and Stockmeyer, From FOCS 1972. Oh. I guess that proves that its NOT natural.

This story raise the question—what is natural? Do we need that someone worked on a problem beforehand to make it natural? Is it good enough that they should have worked on it? Or that they could have? Logic has the same situation with the Paris-Harrington results of a result from Ramsey Theory that is not in Peano Arithmetic, but the first time it was proven was in the same paper that proved it was not provable in PA.

Incidentally, there are more natural problems that are not in P. Some games on n by n boards are EXPSPACE or EXPTIME complete and hence not in P. Would have been a better answer, though it would not have made as good a story.

More FOCS News

Fair and balanced coverage from Adam Klivans

To answer one of Lance's previous posts, the Internet is definitely harming conferences: most everyone who stayed up until 5 AM to watch the Red Sox beat the Yankees in 14 innings on MLB.TV has not made it to James Lee's talk at 8:30 AM on embeddings (in fact I think I'm the only one who did make it here). Krauthgamer, Lee, Mendel, and Naor presented a powerful new method for constructing embeddings of finite metric spaces called measured descent which, among other things, implies optimal volume-respecting embeddings (in the sense of Feige).

I checked the registration numbers and indeed only 172 people have officially registered for the conference—that's 100 less than the registration at STOC in Chicago.

Yesterday I mentioned the winners of the best paper award. I should also mention the best student paper award winners: Lap Chi Lau's An Approximate Max-Steiner-Tree-Packing Min-Steiner-Cut Theorem shared the prize with Marcin Mucha and Piotr Sankowski's Maximum Matchings via Gaussian Elimination. Lau's paper gives the first constant factor approximation to the problem of finding a large collection of edge-disjoint trees that connect an undirected multigraph. Mucha and Sankowski give a nice method for finding maximum matchings in general graphs in time O(n^ω) where ω is the matrix multiplication exponent. Lovász showed how to test for a matching in a graph using matrix multiplication, and Mucha and Sankowski extend this and actually recover the matching.

Valiant's talk on Holographic Algorithms was well attended: he described a new, quantum-inspired method for constructing polynomial-time algorithms for certain counting problems. The algorithms are classical (no quantum required) and give the first efficient solutions for problems such as PL-Node-Bipartition: find the cardinality of a smallest subset of vertices V' of a max-degree 3, planar graph such that deletion of V' (and its incident edges) causes the graph to become bipartite. At the end he gave a simple criterion for proving P = P^#P via these techniques!

FOCS News

Adam Klivans reports from Rome.

Rome is the host city for this year's FOCS conference. While everyone enjoys visiting one of the world's great capitals, attendance at the sessions can occasionally suffer, and the sessions this year do seem noticeably smaller. Another explanation could be the the high cost of traveling to and staying in Rome. On the plus side, I get to see many European theorists of whom I had known in name only.

For those who did make the trek to the southern tip of the Villa Borghese, the first day featured the presentation of the two results which won best paper: Subhash Khot's Hardness for Approximating the Shortest Vector in Lattices and Applebaum, Ishai, and Kushilevitz's Cryptography in NC⁰. Subhash was an author of two other impressive hardness results in the same session: Ruling Out PTAS for Graph Min-Bisection, Densest Subgraph and Bipartite Clique (the title is self-explanatory) and Optimal Inapproximability Results for Max-Cut and Other 2-variable CSPs? (with Kindler, Mossel, and O'Donnell) which gives evidence that the Max-Cut approximation algorithm of Goemans-Williamson is the best possible.

The cryptography session featured the above Cryptography in NC⁰ paper which Lance mentioned in an earlier post as well as an intriguing result due to Salil Vadhan, An Unconditional Study of Computational Zero Knowledge showing how to establish important properties of computational zero knowledge proofs without assuming the existence of a one-way function.

The controversial topic of what to do with the special issue of FOCS continued at last night's business meeting. It appears as though Elsevier will lose another opportunity to publish a special issue of STOC/FOCS, as a vote last night indicated a strong desire to give SICOMP the responsibility instead (a similar thing occurred at STOC this year).

Some Dagstuhl Presentations

At Dagstuhl Manindra Agrawal presented recent work of his students Neeraj Kayal and Nitin Saxena (the trio that showed a polynomial-time algorithm for primality testing) on rings given by a matrix describing the actions on the base elements. They show a randomized reduction from graph isomorphism to ring isomorphism and from factoring to #RI, counting the number of ring isomorphisms. They also show a polynomial-time algorithm for determining if there are any non-trivial automorphisms of a ring and that #RI is computable with an oracle for AM∩co-AM. Agrawal conjectured that #RI is computable in polynomial time, a conjecture that would imply factoring and graph isomorphism have efficient algorithms.

We also saw a series of presentations by Andris Ambainis, Robert Špalek and Mario Szegedy. Ambainis described his improved method for showing lower bounds for quantum algorithms that provably beats the degree method. Špalek talked about his work with Szegedy showing that Ambainis techniques as well as different tools developed by Zhang, Laplante and Magniez, and Barnum, Saks and Szegedy all gave the same bounds. Szegedy, in his presentation, called this measure the div complexity and showed that the size of a Boolean formula computing a function f is at least the square of the div complexity of f.

Is the Internet Harming Dagstuhl?

Dagstuhl was designed as a place to bring a small group of researchers to an isolated environment where they could give some talks, discuss research and otherwise socialize among themselves free from other distractions. No televisions though a radio bought to hear news during the 1991 Gulf War. We could get two-day old news from America via the Herald Tribune. While they had computer rooms, in the early days we had no world wide web and email was far less used. Instead we had rooms for coffee, rooms for beer and wine, rooms for billiards and music and rooms just to hang out. Everyone stayed on premises and we had no phones in rooms, just a couple communal phones to call home.

Although Dagstuhl has expanded, rooms not only have phones but WiFi throughout. We can answer email, read news, write weblog posts (as I am doing now) from the comfort of our own isolated desks. We're watching baseball games and the debate over the internet. But worse than being connected, the rest of the world knows we're connected. I find myself having to take time to fix problem sets for my class and deal with departmental issues as do many of my other colleagues here.

The internet has greatly helped science by bringing us closer together but also prevents us from being disconnected losing many of the advantages of these workshops. A sign here proclaims "Are you here for computer networking or human networking?" Something to remember next time you go to a conference.

Back in Dagstuhl

I'm back in Dagstuhl for the workshop on Algebraic Methods in Computational Complexity. The roof looks great. I have attended several Dagstuhl workshops for over twelve years now since the workshop on Structure and Complexity Theory in 1992. I have seen Dagstuhl expand and evolve over these years and this is the first time I feel that Dagstuhl has achieved its completed state. I love coming here; Dagstuhl has a contained environment in a pretty but boring part of Germany where we complexity theorists give seminars, eat and drink together and talk science and other stuff. Politics and baseball seem to dominate the discussions this week.

A group of German software engineering professors share Dagstuhl with us this week. They are meeting to discuss future directions of German software engineering research and to find ways to increase student enrollment. The drop in students desiring a computer science degree is not just an American phenomenon.

A Celebration of Women in Computing

A report from Varsha Dani.

The Grace Hopper Celebration of Women in Computing was held in Chicago on October 6-9. This was the fifth such conference, since its inception in 1994. This year there were over 800 attendees from all over the country.

This conference is a forum for discussion of issues faced by women and a showcase for achievements of women in the fields of computing and technology. There were a number of talks on social issues, some technical presentations by young investigators, and a few invited technical talks. There were also a number of social and networking events hosted by IBM, Microsoft, Google and others.

Among the invited talks, there were three I particularly enjoyed.

Jessica Hodgins of CMU talked about connections between ideas in robotics and computer graphics and animation, especially simulation of human movements.

Cynthia Dwork of Microsoft Research spoke about the problem of publishing (transformed) data from public databases (such as census data) so as to maintain a balance between the utility of the published information and the protection of the privacy of individuals represented by the data. Her approach to privacy is influenced by ideas from cryptography.

Daniela Rus of MIT spoke about self-reconfiguring robots. These robots are distributed systems, consisting of a number of identical modules which can dynamically adapt the way that they are connected to each other to best fit the task at hand.

NP-Completeness for a 9-Year Old

My nine-year old daughter had a homework problem with the following diagram.

She had no problem solving questions like: Beginning and ending at the entrance, describe the shortest route you can take that will allow you to see 4 different kinds of animals.

"You're doing computer science," I said.

"I don't see any computers," she responded.

"Computer science is problem solving like finding the shortest path."

"Then computer science is pretty easy."

"OK, is there a way to visit every animal exactly once?"

She found this question much more challenging.

Groups versus Departments

In the US the terms Assistant Professor, Associate Professor and Professor represent different stages in one's career but they all play a similar role in research and advising students. An assistant professor is nobody's assistant.

The names get their meaning from a structure you still see in many other countries (Germany is a good example). Here you have research groups, where a lead professor has nearly complete control of hiring and the budget. The equivalents of assistant and associate reflect the temporary and permanent faculty members of those groups.

How does this affect graduate studies? In Germany a grad student joins a group and works within that group. In the United States a student joins a department usually without a specific advisor in mind and often not initially committing to a specific subfield of computer science.

So to those who send me and other American computer scientists requests to join our groups, the US system doesn't work that way. Instead go to the departmental web page and follow the appropriate links to find information on how to apply to that department. If you have a specific researcher that you want to work with, use the personal statement to say this and your reasons for it.

Trust me, we read the applications carefully and choose Ph.D. candidates as best as we can. It just doesn't help to send personal requests, I just point to our web page and trash the email.

Holy Trefoils, Math Fans!

Can one use a comic book and a toy to teach a complicated subfield of mathematics? Why knot?

Larry Stockmeyer Commemorations

Ron Fagin asked me to announce two public commemorations of Larry Stockmeyer and his work.

The first will be held at the IBM Almaden Research Center on Monday, October 25, 2004.

The second will be held in conjunction with STOC '05 in Baltimore on May 21-22, 2005.

Please join the community in honoring the memory of one of the great complexity theorists.

Are we too nice?

Steve Smale talked about his experiences in the Economics Theory Workshop at Chicago, particularly the aggressive questioning. I didn't attend his talk but I did go to a few of the econ theory seminars years ago and it forms an interesting contrast to the CS theory talks which have few usually technical questions followed by polite applause.

The econ theory seminar took place in a medium-size conference room with a long table. Graduate students sat in chairs along the walls. The speaker was at one end of the table and econ professors, usually including multiple Nobel prize winners, around the rest of the table. A copy of the paper was sent with the talk announcement and almost from the first slide the faculty aggressively attacked the speaker with questions about the validity of the model or the importance of the results. (Remember this was the theory seminar, imagine the questions at the political economics seminar). At the end of the seminar time, the talk ended and everyone left the room. No applause.

I don't recommend that we follow this model in theoretical computer science. However we usually go to the other extreme and (outside of crypto) rarely ask negative questions in a seminar. Typically the only negative feedback we get in our field is from anonymous referees and reviewers. If we were forced to defend our research in an interactive setting, we would establish a better understanding of the importance of the models and results of our own research.

The Specialization of Computer Science

I heard the following from a senior economist recently.

A researcher at the beginning of his career has to please others. In order to receive a Ph.D., get a job and eventually tenure, he has to not only produce good research but research of value to others. The researcher might think that once he gets tenure he can do the research he wants, but by that time he has become so specialized it is impossible to change direction.

Looking at economics can give us a glimpse into the near future of computer science as a discipline. Though economics as a field has been around for a very long time, only since the 1950's did economics develop as a rigorous mathematical discipline. This gives economics about a 15-year head start on computer science.

When I started in grad school in the mid-80's, I could follow nearly every talk at the major theory conferences, STOC and FOCS, though I would not have followed any computer science talk which might have been true 10-15 years earlier. These days I can understand the importance of the main results of maybe half of the talks and have actual interest in only a small fraction of these. The growth of specialty conferences such as Complexity, SODA (algorithms), SoCG (Computational Geometry), Crypto, RANDOM/APPROX, COLT (Learning Theory), LICS (Logic in CS), QIP (Quantum) and so on have only increased this divide. We get less and less crossbreeding between these subfields of theory.

On the other hand, some researchers still can and do (with some effort) change research areas in theory and general computer science even after tenure. But in 15 years will we look like economics where a late change in field is difficult to impossible and soon after that like mathematics where it often takes years of graduate school just to understand the major open questions in an area.

Computer Science's Newest Genius

Congratulations to Daphne Koller, this year's MacArthur Fellow in computer science. Koller uses a strong mathematical approach to decision making and learning.

Republicans and Democrats on Science Research

From a comment on my last post.

I think most computer scientists, even conservatives vote Democrat for one reason. Democrats fund the NSF, and the NSF gives us fat paychecks.

From discussion I have with other computer scientists, I don't find science funding a major factor in their voting decisions. On top of that the preface doesn't hold water. I went and computed the average yearly increase in the NSF budget during the tenures of the last several presidents.

• Carter, 7.9%
• Reagan, 11.0%
• Bush Sr., 10.6%
• Clinton, 7.6%
• Bush Jr., 9.1%

The Democratic and Republican platforms have similar goals in scientific research though the Republican platform goes into more detail. From the Democratic Platform:

We will invest in the technologies of the future, from renewable energy to nanotechnology to biomedicine, and will work to make permanent the research and development tax credit. We will achieve universal access to broadband services, which could add $500 billion to our economy, generate 1.2 million jobs, and transform the way we learn and work. And we will put science ahead of ideology in research and policymaking.

The Republican Platform takes two pages to give the same ideas (except for that last sentence). Here is the section on Research and Development.

America's economy is undergoing a fundamental transition from one based primarily on manufacturing to one based on innovation, services, and ideas. Two-thirds of America's economic growth in the 1990s resulted from the introduction of new technology and 60 percent of the new jobs of the 21st century require post-secondary education, yet only one-third of America's workforce has achieved that level.

In order to maintain America's global leadership, Republicans have provided unprecedented support for federal research and development to help spur innovation. Federal R&D funding is up 44 percent from 2001 to $132 billion in 2005, which includes a 26 percent increase in support for basic research. The President has doubled the budget for the National Institutes of Health and increased the National Science Foundation budget by 30 percent. President Bush and the Republican Party also support making the R&D tax credit permanent.

The rapid pace of technological development demands that we remain on the leading edge of innovation and science. Republicans are committed to providing the investment and incentives needed to foster next generation technologies. The 21st Century Nanotechnology Research and Development Act, passed by a Republican Congress and signed by President Bush, increased funding for nanotechnology research. In addition, the President has dedicated $1.7 billion over five years to develop hydrogen fuel cells and related next-generation energy technologies. The President's support for NASA and vision for space exploration will also enhance scientific development and technological breakthroughs.

In short the parties do not differ much on a future research investment. Both platforms also push science education. The Republicans have had a better historical record of science funding but Bush has come under fire for ignoring science in policy making. Better not to worry about science and use other factors in your choice of president.

The Blue State of Science

I usually avoid politics in this weblog but I cannot totally ignore the US presidential election happening slightly more than a month from now. But nothing I will say would make much difference; nearly all computer scientists, and I expect most scientists, will vote for Kerry (or would vote for Kerry if they were US citizens). It's not based on a single issue. If we never went to war in Iraq, the economy were booming, Osama Bin Laden was behind bars and Bush supported a woman's right to choose, you would all still vote for Kerry.

What makes scientists so liberal? Why doesn't a field like computer science draw from a wide political spectrum? Does this liberal attitude stifle real political debate in scientific departments or even worse discourage those with more conservative views from entering our field?

NP-Completeness is Illuminated

Another literary reference to a hard combinatorial problem. Jonathan Safran Foer describes plans for a wedding reception in his disjointed novel Everything is Illimuniated.

The hardwood floors were covered in white canvas, and tables were set in a line stretching from the master bedroom to the kitchen, each feathered with precisely positioned name cards, whose placement had been agonized over for weeks. (Avra cannot sit next to Zosha, but should be near Yoske and Libby, but not if it means seating Libby near Anshel, or Anshel near Avra, or Avra anywhere near the centerpieces, because he's terribly allergic and will die. And by all means keep the Uprighthers and Slouchers on opposite sides of the table.)

The Beauty of the Magic Number

Baseball has a large number of mathematical nuggets but since my childhood I have always liked the simplicity of the magic number. In a division race, the magic number is the minimum number of wins by the first place team and number of losses of the second place team to guarantee the first place team wins the division.

Let's do an example. As I write this the New York Yankees have 94 wins, the Boston Red Sox have 60 losses. The easiest way to compute the magic number comes from working backwards from the definition. There are 162 games in a season so the Yankees magic number is 162+1-(94+60) = 9. Any combination of nine Yankees wins and Red Sox losses and the Yankees wins the American League East. The "+1" comes from the fact that in a tie the Yankees would still need to win a one-game playoff to win the division.

What can the magic number teach us about complexity? Consider the RIOT Baseball Project at Berkeley. Not satisfied with the magic number, the project computes the First Place Clinch Number as the "Number of additional games, if won, guarantees a first-place finish." To compute this number one has to look not only at the current standings but the schedule of remaining games between the teams.

My main issue of the clinch number relates to complexity. Not only is it more complicated to compute; to update the clinch number after a game sometimes requires recomputing the number from scratch. The magic number has a simple update function counting down like a rocket launch. Yankees win the magic number drops by one. Red Sox lose the magic number drops by one. If the Yankees beat the Red Sox, both events happen so the magic number drops by two. And once the magic number hits zero you pop the champagne. That's the beauty of the magic number.

Quantum in the North; Random in the South

A couple of interesting workshops happening this week both studying information, not the usual classical notions of information but quantum and random information.

At Banff in the Canadian Rockies we have the BIRS Workshop on Quantum Computation and Information Theory. This workshop will examine the properties of quantum information and tie it together with people working on quantum algorithms and complexity.

Meanwhile in Córdoba, Argentina on the edge of the Sierra Chica mountain is the Conference on Logic, Computability and Randomness 2004. Much of this conference focuses on random sets, not from a probability distribution but single sets that "look" random. Rater surprisingly, whether we define random sets by passing statistical tests, foiling betting strategies or using Kolmogorov complexity, these notions often lead to equivalent definitions of random.

While circumstances keep me in Chicago I say to the participants of both meetings: Enjoy the mountains and save some theorems for me.

NSF News

Arden Bement, who has been serving as the acting director of the National Science Foundation since Rita Colwell stepped down in February, has been nominated for the permanent director position.

The US Senate continues to work on the appropriation bills to set funding levels for next years US fiscal year that starts October 1. The CRA has a summary of the various bills affecting research funding in computer science (see also this note from AIP). Most worrisome (as I've mentioned before) is the funding for the VA-HUD bill that covers the NSF. The House committee would cut the budget by 2%. The CRA has an Advocacy Alert, still time to contact your senators.

Email's Curse of Success

Computer Scientists have communicated via email since the mid-1980's. Back then email worked quite well: You would send a message and usually get a quick response. We avoided telephone tag, trying to reach each other by phone when we needed to talk to each other quickly. Research ideas spread quickly; the world became smaller. Even within a department communication became paperless as one can get a message out to everyone far quicker electronically.

So what went wrong? We still use email today as the primary source of communication among computer scientists. But send a message today and I've learned to wait on average a couple of days to expect a response, if I get one at all.

Spam is the obvious culprit. Spam does clog our inboxes and even worse many of us don't carefully go through our spam folders and some legitimate mail gets unread. Spam has also made some computer scientists reluctant to share their email addresses online. But spam is not the only issue.

Email has become the communication of choice in the rest of the world as well. Besides messages from other scientists, I get email about my daughter's soccer team, announcements of upcoming concerts, warnings from the local police departments, a morning summary of the New York Times, financial information, utility bills and much more. All legitimate and usually useful email but it takes longer to work through it and slows down the time to respond to other scientists. Not to mention the many other web distractions such as news and weblogs (So stop reading this blog and respond to my emails. You know who you are.)

I can't rely on older technologies; since computer scientists expect email they check even less often their phone messages and postal mail. I can't rely on newer technology; computer scientists are surprisingly slow in adapting to new tools (like mail attachments) and it'll be years before instant messaging becomes common in the scientific community.

Oddly enough in our highly connected society it becomes harder and harder to get someones attention. So what am I doing? Slowly collecting the cell phone numbers of other computer scientists. Want mine? Send me an email.

Is the AP Test to Blame for Shifting CS Enrollments?

It is no secret that undergraduate enrollments in computer science have been dropping over the past five years. Students follow the money and, with the perception of a weaker job market in computer-oriented careers, less students are willing to study computer science.

Why does computer science follow the job market so closely? We don't see such swings in physics or history but such swings are common in engineering disciplines. Are undergraduate viewing computer science more as engineering than science? And why?

One theory I recently heard puts the blame on the Advanced Placement (AP) Computer Science Exam given to high school students. The reasoning goes as follows: The AP exam has a strong emphasis on the Java programming language and so high school teachers, teaching to the exam, focus most of their course on syntax and coding of Java. This gives the impression to students that computer science = programming.

I don't agree with this assessment. I looked at some sample CS AP tests. The tests, particularly the AB exam, requires some knowledge of data structures and simple algorithms. Nothing deep but enough that students should realize that computer science is more than just programming.

There was a surge of interest in computer science when I started college in the early 1980's (with the advent of personal computers) before an AP test in Computer Science even existed. Also I've heard of declines in enrollments outside the US where they don't use the AP tests.

But in the end we shouldn't be that worried about shifting enrollments. Advances in computer technology have helped drive computer science from a virtually non-existent discipline forty years ago to one that many universities now consider one of their most important departments. Better to have enrollments that swing up and down with the state of the computer industry than one that stagnates at the low end.

Favorite Theorems: List Decoding

August Edition

In coding theory, one typically maps a string to a code such that with some small amount of error in the code one can still recover the original string. What if the amount of error is too much to give a unique decoding? In the 1950s Peter Elias suggested the idea of list decoding, coming up with a short list of possibilities one of which is correct.

Madhu Sudan showed that list decoding can be achieved in scenarios where one cannot do unique decoding.

Decoding of Reed-Solomon Codes Beyond the Error-Correction Bound by Madhu Sudan

In this paper Sudan gives a polynomial-time list-decoding algorithm that can deal with errors in the code beyond what regular codes can handle. Later Guruswami and Sudan give a polynomial-time algorithm that handles what is believed to be the best possible amount of error.

List-decodable codes have had applications to many areas including pseudo-random generators, extractors, hard-core predicates, probabilistically-checkable proofs and a neat result by Sivakumar on the implications of SAT being membership-comparable.

We've seen many other important papers in coding theory from computer scientists over the last decade. Besides the work on list decoding I should also mention Spielman's breakthrough result showing linear time encodable and decodable codes building on the initial work of using expander graphs for codes developed by Sipser and Spielman.

For much more on coding see the surveys by Sudan on List Decoding and Guruswami on Error-correcting codes and Expander Graphs.

Which Affiliation?

Dieter van Melkebeek and I had a mild disagreement over an issue in writing a paper and he suggested I discuss it on my weblog. So here goes.

We're working on a journal version of a paper where we did the research back when we were both in New Jersey (Dieter is now on the Wisconsin faculty). Dieter listed our current institutions on the paper. I think that we should list our institutional affiliation when we performed the research, or more precisely the place paying the salary at that time. I don't feel that strongly about the issue so I am letting Dieter have his way, especially since he did the vast majority of the writing. I did ask that we have footnotes explaining our affiliations at the time of the research. (As a side note, footnotes should also contain other support information such as grants, where one was physically located when the research was done if different and contact information, though these days one needs only know how to spell my name correctly when using Google).

So I'll open this up to my readers. Which affiliation should one use? Or are we just arguing over an issue that nobody really cares about?

Just Because I'm a Scientist Doesn't Mean I Know Anything

My six-year old daughter playing with her friend on the computer ran into some problems. So she found me in the house and said, "Daddy, I know you are a computer scientist so you know everything about computers and we need you to fix our game."

I've learned to expect this attitude from adults. Often when I talk to a non-academic about being a computer scientist I get responses like, "Should I get Windows or a Mac?", "I was thinking of setting up a wireless network." or "What do you think of that Google IPO?". Of course this is on top of them thinking I have a cushy academic job teaching three hours a week with summers off.

For my daughter I just went ahead and fixed her problem. I know when she becomes a teenager she'll run circles around me on the computer and will say "When I was a kid I thought you knew everything about computers. What do you computer scientists do anyway?" Then we can talk.

The Electoral College

As everyone knows from the 2000 election, the United States does not use a majority rule to choose the president, rather they use a more complicated system known as the Electoral College. With some calls for the abolishment of the Electoral College, let's take a look at the College from a computer science point of view and see the rather clever device our founding fathers have created.

In short the Electoral College works as follows: 538 electors are allocated to states as the sum of the senators (2 for each state) and representatives (proportional to population). In most states, each voter picks a single candidate and the candidate that wins the most votes receives all of the electoral votes for that state. The candidate winning the majority of the electoral votes becomes president. More details here.

In computer science terms (assuming two candidates), we have a weighted majority of majorites or a depth-2 neural net. It has some properties that you would want:

• Monotonicity: If a candidate wins the election and more people vote for him, he will still win.
• Fairness: Barring a tie, if all the votes were switched the other candidate would win.

The College does lack symmetry, a permutation of the voters could lead to a different result. Only the simple majority function has symmetry, monotonicity and fairness. But symmetry is not necessary for an election scheme.

The United States is just that, a collection of fifty states each with their own laws, cultures and economies, united under some common principles. A simple majority would have the large populations centers overwhelm the rest of the country in choosing our leader. A majority of majorities would give some states far more power than their size would dictate. So a compromise was formed, a weighted majority of majorities to give small states some but not too much influence. The fact that this process does not always agree with majority is not a bug but a feature that preserves the balance between small and big states, rural and urban America. It also keeps balance between states of the same size, an lopsided vote in California would not overwhelm a closer vote in New York.

Some things I would change in the Electoral College: Electors should be required to vote for the candidate they represent; for each state we should have a ranked voting method instead of plurality takes all; the tie-breaking rules should be changed, now they give too much power to the small states.

The winner of the World Series in baseball is not the team that scores the most runs but the team that wins the most games, a majority of majorities and most people feel it gives a better indication of the better team. Why shouldn't elections deserve a system at least as sophisticated?

Is Encryption Doomed?

Considerable Slashdot discussion about a Technology Review article Is Encryption Doomed? subtitled Our entire information society rests on a fragile foundation that mathematicians are racing to dismantle.

That fragile foundation is the P versus NP question. Much of current cryptography is based on the NP problem Factoring which would have an efficient algorithm if P were equal to NP. If P = NP than no other method of public-key cryptography would be possible either. However, as I have argued before, the loss in public-key crypto would be greatly offset by the gain in efficiency of nearly every other aspect of our lives. Encryption's doom would be society's gain.

Factoring is not believed to be NP-complete and we could have the worst of all possible worlds with no cryptography and no new algorithms for problems we care about, one of five possibilities explored by Russell Impagliazzo.

Racing to dismantle is a bit of an overstatement. First of all we have nothing to worry about. As Juris Hartmanis once said, "We all know that P ≠ NP, we just don't know how to prove it." Remember too that all mathematics is based on unprovable assumptions about consistencies of logical theories. Doesn't seem to seriously bother anyone.

The article quotes Adleman as saying "From my perspective, we are no nearer to solving the problem now that we were when bell-bottom pants were cool." Adleman is an optimist; we do not even currently have a good approach to showing P ≠ NP. We are much further away from solving the problem than ever before.

Theory in the Coca-Cola Capital of Iowa

  

Today I gave the talk at the Atlantic Theory Seminar, not Atlantic as in ocean but Atlantic, Iowa (population 7,257). Located halfway between the theory groups of Iowa State and Nebraska, the Cass County branch of the Iowa Western Community College hosts a theory seminar every couple of months. Pretty impressive that these theory groups, faculty, postdocs and students, drive two hours each just to join for a seminar and talk theory with each other. Quite an enjoyable day in rural America.

Sorry about the quality of the picture above. We didn't have a digital camera so I took the picture with my cell phone.

Computationally Simple One-Way Functions

An upcoming FOCS paper is drawing a lot of interest at TTI and Chicago, Cryptography in NC⁰ by Benny Applebaum, Yuval Ishai and Eyal Kushilevitz.

Don't let "NC⁰" scare you, it simply means that every output bit depends on a constant number of input bits. In this paper the authors show that under reasonable assumptions one can have one-way functions and pseudo-random generators where each output bit depends on only four input bits. Quite surprising that such simple functions can be so hard to invert.

Their proof uses a clever but not overly complicated reduction using randomized polynomials from a larger class (⊕L/poly) to NC⁰ and so if one-way function and PRGs exist in the larger class than slightly weaker versions exist in NC⁰ respectively. The larger class contains many functions conjectured to be one-way or a PRG, including those based on factoring.

I remember Mike Sipser mentioning in a complexity class I took back in the mid-80's that "We don't even know how to show there are no one-way functions in NC⁰." Now we know why.

What happened to the future?

Disney World has two areas originally designed to give a glimpse of "the future", Tommorowland in Magic Kingdom and Future World at EPCOT, which itself once stood for Experimental Prototype Community of Tomorrow. These areas give somewhat a nostalgic view of the future from the time of my childhood but not of the future from today.

Not only has society's view of the future changed but even the view about the future has changed. We live in an era of massive changes in technology particularly in access to communication and information. In the "Spaceship Earth" ride that shows the history and future of communications, the future shows two kids seeing and playing games with each other through video monitors, a task easily accomplished today with webcam-equipped networked PCs. But the ride missed many aspects of computers and the web. Who would have thought when I was a kid that I would now be writing this post on a commuter train that soon will be read around the world.

On the other hand we also dreamed of flying cars and space planes but the technology of transportation has not significantly changed since I was born and I don't expect major changes in the next forty years. So the future has come but not quite as we expected.

Technology has made the world a more homogeneous place. When at the Norway pavilion at EPCOT, an American visitor asked a Disney worker from Norway about what the country was like to visit. "The towns are like mid-size American cities" was the reply. I guess it is a small world after all.

ε and the Olympics

Back from Disney World and ready to tackle the new academic year. Thanks to Adam Klivans for his guest posts. Interesting to see that COLT glorifies the open problems. In complexity we prefer to see them closed.

Varsha Dani emailed a note about an article describing an Amazon tribe with no concept of numbers. I guess they don't send anyone to the olympics where numbers seem king.

Watching gymnastics I am always amazed how winning seems to depend on sticking the landing. After a rather complicated and lenghty routine why should whether your feet move at the end be the difference between Gold and Bronze? The answer lies in the ε; the best gymnasts can uniformly hit the major elements of their routines but consistently sticking the landing is much more difficult and that what makes or breaks the result.

We see the ε issue in many scenarios, most notably the 2000 US presidential election where confusing ballots in one county created a huge controversy. The budget of the NEC Research Institute is miniscule compared to the revenue of NEC corporate. A couple of years ago NEC eeked out a profit about the same size of the cost of the Institute and all of a sudden the NEC Research Institute looked very expensive to NEC. In another example, consider the relatively large power a small party can have in a coalition in a parlimentary system.

The best way to avoid the ε problem is by decisive victories. Solidly beat your opponent in an election or have enough parlimentary seats so you don't need small partners. Make enough of a profit so that a cheap research lab stays that way. One only gets the ε problem when one has a statistical tie and then the small things take on great importance.

In gymnastics one would want a system where a greatly superior gymnast can score high enough that a small jump on the landing won't make a difference. But the current system doesn't allow that; with a top score of 10 the world's best gymnasts all get well over nine, making it impossible to put enough of a gap between a the best and the rest.

"Conclusions and Open Problems" (by Adam Klivans)

Unless Lance has been involved in some unfortunate roller coster accident, this is most likely my last post. It remains to be seen whether I will be allowed to keep my posting privileges here on the board (place your bets on "No"). What I've taken away from this experience, more than anything else, is that posting every day is a tremendous time sink. Lance, kudos to you for the almost daily missive.

At the end of most technical talks is the obligatory "Conclusions and Open Problems" slide, usually the least thought out moment of the presentation, which consists of a brief summary of the talk and a list of the most obvious (difficult) open problems. For the last few years, COLT has glorified the open problems section and allocates about an hour of time for a presentation of open problems. The open problems themselves must be submitted months beforehand and are refereed (how rigorously is anyone's guess); accepted problems appear in the proceedings. A list of this year's open problems can be found on the COLT 2004 program schedule -- the session was held on Friday evening.

Are there any other computer science conferences where open problems are refereed and given their own slot in the program? It always seems to work out well at COLT, and while I am aware of open problems being presented at rump sessions at various conferences, I don't know of other venues which require advance submission of problems.

With that, gentle reader, I return you to Lance's wise embrace. If I ever get to guest blog again, I will reveal what's hidden in Lance's "Private" directory here on fortnow.com. Some "lost" theorems apparently-- here's an aborted post entitled "Soon I will be famous: a simple proof that NP = coNP" -- and here's another unfinished note with some not so nice things to say about Algorithms. And what's this? A love letter to Jessica Simpson? Oh if only we had more time.

Constant Depth Circuits, Fourier Transform, and Learnability (by Adam Klivans)

First, thanks to Jeff Erickson for the lone comment on my previous post. For a second I was worried that I would have to post about Quantum Learning to bait Scott Aaronson into commenting. Fortunately, we're past that. I also realize now that being in Chicago I'm just a two hour drive away from you Jeff at UIUC. Maybe you, Ernie, and I should get some 3-D hotcakes at the local Waffle House-- on me.

Many top notch researchers come to visit the Toyota Technological Insitute here in Chicago. This fall alone Lenore Blum, Bruno Codenotti, Prahladh Harsha, and Jaikumar Radhakrishnan will be in residence along with TTI's regular faculty.

Yishay Mansour visited in August for about two weeks, and I had the chance to ask him about his work along with N. Linial and N. Nisan which pioneered the use of discrete Fourier analysis in computational learning theory. The paper Constant Depth Circuits, Fourier Transform, and Learnability gives a quasi-polynomial time learning algorithm for constant depth circuits with respect to the uniform distribution. More importantly, it pointed out a connection between the Fourier concentration of a Boolean function and its learnability.

If f is a Boolean function, we could imagine writing f as a multilinear polynomial in n variables mapping {-1,1}^n to {-1,1}. Every Boolean function can be written as such a polynomial whose total degree is at most n. Each coefficient of this polynomial measures the correlation of f with that monomial. These are the Fourier coefficients of f. Linial, Mansour, and Nisan showed that if the sum of the squares of the coefficients of monomials of degree d and larger is small, then there is an n^{O(d)} time algorithm for learning f with respect to the uniform distribution-- roughly speaking it is sufficient to estimate the coefficients of only the low degree monomials and output this polynomial.

What does any of this have to do with constant depth circuits? They also proved that for any circuit of depth d, the sum of the squares of the coefficients on the terms of degree (log n)^d and higher decays rapidly. From the above paragraph this gives us a quasi-polynomial time algorithm. For a rough intuition as to why this is true, consider one implication of Hastad's Switching Lemma, namely that parity cannot even be approximated by constant depth circuits. Thus every coefficient of a sufficiently large monomial (each monomial is a parity function) must be small.

As it turns out, according to Yishay, the work stemmed from an effort to prove circuit lower bounds, rather than a plan to develop new learning algorithms. The authors were inspired by Kahn, Kalai, and Linial's work on the influence of variables on Boolean functions and thought that discrete Fourier analysis might be the right tool for studying circuits. They happened to be correct-- in an unexpected way.

Banff Revisited (by Adam Klivans)

Hey, you're back! And I'm really starting to feel comfortable at this posting gig. Thanks for all of the comments I got about my previous post-- all zero of them.

A few weeks ago Lance reported on the events from a complexity workshop he was attending at the Banff International Research Station, an institute similar to the International Space Station except that it's in Canada rather than outer space.

What Lance didn't mention was that at the exact same time, some important computer science conferences were taking place just down the street at the Banff Park Lodge. I was participating in the 17th annual Conference on Learning Theory (COLT) which was co-located with the International Conference on Machine Learning (ICML) and the Conference on Uncertainty in Artificial Intelligence (UAI).

Back when COLT stood for Computational Learning Theory (circa 1988-2002), the conference was known for focusing on the computational complexity of machine learning. Nowadays the conference still operates from a theoretical perspective, but, as the Conference on Learning Theory, the program covers everything from game theory and economics to kernel methods in addition to traditional PAC style results.

A PAC style result that appeared in COLT 2004 which may be of interest to the readers of this web log is Polynomial-Time Prediction Strategy with Almost Optimal Mistake Probability by Nader Bshouty. His paper solves a problem in the online learning setting. In this setting, an unknown function f is chosen from some fixed concept class and at time t a learner is presented with an input x chosen according to some distribution D.

The goal of the learner is to run in time polynomial in log t (and all of the other relevant parameters) and predict the value of f(x) with mistake probability O(1/t) (Haussler, Littlestone, and Warmuth proved that this mistake probability is optimal). Bshouty shows that if the concept class is PAC learnable, then there exists an online learning algorithm which runs in time polynomial in log t and achieves mistake probability O(log t/ t). His algorithm has an exponential improvement in running time as previous solutions ran in time polynomial in t. The algorithm works by iteratively creating a branching program based on hypotheses considered at previous time steps. A boosting-type procedure dictates which branch to take for any new input.

In the spirit of being controversial (Lance asked me to be controversial), I could discuss the pros and cons of the change from Computational Learning Theory to Conference on Learning Theory (as a concrete example of differences in the community, about half the participants at the COLT business meeting wanted to see COLT co-located with STOC in 2006-- University of Washington folks make your move-- and the others wanted to co-locate with ICML). I'll leave that, however, for my faithful readers to debate. I will point out that it's hard to argue with the increase in attendance at COLT over the last few years.

Favorite Theorems: The Harmonic Sieve (by Adam Klivans)

What does Lance Fortnow do after getting a paper accepted to FOCS? He goes to Disneyworld for a week, of course. While Lance blasts pasts celestial satellites on Space Mountain, I will humbly try to replace the irreplaceable.

Considering the topic of yesterday's post, if there were a list of favorite theorems in computational learning theory, a field which makes only brief appearances here on the weblog despite its many connections to computational complexity, Jeff Jackson's algorithm for learning DNF formulas would certainly be on it.

A DNF formula is a Boolean formula written as an OR of ANDs (e.g. x_1 and x_2 OR x_3 and x_5). The size of a DNF formula is equal to the number of terms or ANDs. The problem of PAC learning an unknown polynomial-size (in n, the number of variables) DNF formula with respect to an arbitrary distribution remains one of the most notorious open problems in the field (for background on PAC learning see this post or Kearns and Vazirani's excellent book An Introduction to Computational Learning Theory).

In fact, even if we restrict the underlying distribution on examples to be the uniform distribution, the fastest algorithm for learning DNF formulas runs in quasi-polynomial time (a result due to K. Verbeurgt-- the main idea being that only terms of logarithimic length have a chance at being satisfied, so longer terms can be ignored).

If, however, we allow the learner to make queries to the unknown DNF formula, i.e. if the learner can choose any input x and ask for the value of the DNF formula evaluated on x, then the learner can succeed in polynomial-time.

The solution, due to Jeff Jackson in 1994, shows how to learn polynomial-size DNF formulas with respect to the uniform distribution in polynomial-time (again assuming the learner has query access to the unknown DNF). His algorithm, which he has called the Harmonic Sieve due to its use of Fourier analysis, builds on work due to Blum, Furst, Jackson, Kearns, Mansour, and Rudich (``Weakly Learning DNF and Characterizing Statistical Query Learning Using Fourier Analysis'') which showed that for any DNF formula with s terms, there exists a parity function which agrees with the DNF formula on roughly a 1/2 +1/s fraction of inputs.

The next step of the algorithm involves a novel application of Boosting algorithms (see this post for more on Boosting) for combining these parity functions to obtain an accurate hypothesis. The output of the Harmonic Sieve is not a DNF formula but a threshold of parity functions.

The Harmonic Sieve is one of the rare examples in computational learning theory of a polynomial-time algorithm for an expressive concept class. It is natural to ask whether the queries are essential for the algorithm. Unfortunately it seems like the answer is yes-- we do not know how to learn decision trees or even juntas (both strictly weaker concept classes than DNF formulas) in polynomial-time with respect to the uniform distribution unless the learner has query access to the unknown function. Removing the dependence on queries would be a real breakthrough.

By the way, the interface on blogger.com is worse than I ever could have imagined. Apologies in advance for formatting errors.

Favorite Theorems: Parallel Repetition

July Edition

Consider a simple Arthur-Merlin game: Arthur probabilistically chooses a string r sends it to Merlin who responds with y and then Arthur runs some algorithm A(r,y) to decide whether to accept. Merlin's goal is to achieve the highest acceptance probability possible p for Arthur. Suppose we run the game twice in parallel, Arthur sends r₁ and r₂ and Merlin sends y₁ and y₂ and Arthur accepts if A(r₁,y₁) AND A(r₂,y₂). The highest possible acceptance probability will be p².

Now consider the MIP model with two Merlins M₁ and M₂ who cannot communicate with each other. Arthur sends u and v to M₁ and M₂ respectively who respond with y and z. Arthur accepts based on some function A(u,v,y,z). Once again M₁ and M₂ try to achieve the highest possible acceptance probability p. Now we run the game twice in parallel, Arthur sending u₁ and u₂ to M₁ and v₁ and v₂ to M₂ receiving y₁ and y₂ from M₁ and z₁ and z₂ from M₂ and accepting if A(u₁,v₁,y₁,z₁) AND A(u₂,v₂,y₂,z₂).

One might assume that the best the provers can achieve is p² (an assumption in fact made in an early paper co-authored by a certain weblog author) but in some circumstances the provers can do better. However Ran Raz shows that if p is less than 1, one can get an exponential decrease in p with a polynomial number of parallel rounds in

A Parallel Repetition Theorem by Ran Raz

This paper settles one of the more perplexing aspects of multiple prover proof systems with a highly complicated proof. The result also plays a critical role in reducing the number of queries in probabilistically checkable proof systems which led to some optimal approximation bounds.

As a side note I am off on vacation tomorrow and Adam Klivans will guest blog in my absence. Enjoy.

Wisdom of Crowds

Keeping with this week's theme of prediction, I just finished reading The Wisdom of Crowds written by New Yorker writer James Surowiecki. The book makes the case that large groups can make great decisions, often better than any individual in a group, if three conditions occur:

1. diversity of the members of the group,
2. independent opinions of the group members, and
3. a method for aggregation of the opinions.

Surowiecki's very readable book gives many examples where group decisions do quite well (sports betting, Google's search techniques based on other's web pages, Linux) and where group decisions fail (stock market bubbles, committee meetings, strong CEOs).

Chapter 8 is devoted to science and how many widely spread scientists developing and criticizing various theories lead to explosive growth in our understanding. He also notes that this ideal world has its flaws as unknown researchers have a harder time selling their work than more established scientists.

I don't agree with all the conclusions drawn by Surowiecki but he does lay out what we need to do and not do to benefit from the pooled knowledge of a group. We can also draw lessons in computer science as computation and information gets more distributed that we need to integrate to find the best solutions we can.

Fun with Information Markets

Just over a year ago the Department of Defense cancelled their program on using markets to predict future world events, an overreaction that stopped funding a potentially powerful prediction tool. Robin Hanson has a comprehensive web page giving a history and plenty of links.

Information markets live in limited academic-based markets like the Iowa Electronic Market and offshore sites like Tradesports. For example the current price on Tradesports for Bush winning the election is 51.5 which translates to a 0.515 probability that Bush will win indicating a very close contest.

For each state, Tradesports has a security on whether Bush will win that state. They also have some bundles of states. The price for Florida is 50.1, Ohio 55.4 and Bush winning both Florida and Ohio is 47.1. This gives a surprising correlation between Florida and Ohio. If you believe the theory there is a very high 0.94 probability that Bush wins Ohio given that he wins Florida and with a 0.89 probability these two very different swing states will go the same way.

Tradesports gives David Vitter a 59 percent chance of becoming a senator from Louisiana. David Vitter is the brother of CS theorist and former SIGACT chair Jeff Vitter.

Micromorts

Currently on airplanes children under two can ride free by sitting on a parent's lap. The FAA is considering whether to require such children to have their own seat in a child seat similar to the ones most states require for cars. Sounds reasonable? One argument against goes as follows: If we require parents to pay for a seat for a children there is a chance they will drive instead greatly increasing their risk.

How can we evaluate risk? Decision scientists have developed a measure called micromorts (μmorts). A μmort is a one-millionth chance of death. Sounds gruesome but by counting micromorts we can analyze the right choices to keep the most people alive.

All of three lap children have died in airplane crashes where their parents survived since 1987. The average driver runs the risk of about .02 μmorts/miles. If the average car trip is say 500 miles that translates to about 10 μmorts for each child in the car. Three laptop children have died in airplane crashes where the parent has survived since 1987. This translates to the equivalent of 300,000 car trips or about 15,000/year. About 6 million children ride on laps on airplanes each year, so if more than 0.25% of them were to ride in a car instead because of the higher prices, we would about cost lives by requiring safety seats on planes. My numbers, drawn from various internet sources, don't tell the whole story but nevertheless we can and should do a full analysis before setting policy.

It would be nice to have a list of various activities and how many μmorts they use, say you feel like parachuting, you can get an idea of how dangerous it is compared to say riding a bicycle. But we don't get such lists and people have to use their own judgments and often make the wrong decisions. We can also give a cost amount to a μmort; how much is it worth to save lives?

By finding statistics online you can calculate the risks in your various activities. You need to use about 3 μmort/day on average to keep a 10% chance of accidental death in your life. Spend them wisely.

When to Announce?

Suppose you have some partial solutions of a popular problem. At what point do you announce your results? If you announce your partial results you run the risk of someone else taking your ideas and solving the full problem and you won't get as much credit as you deserve. If you wait and try to extend the work yourself someone else might get the same results you already have and you'll lose or at best have to share the authorship.

If you are completely altruistic you should announce your progress as this will best advance science quickly. But as in the end you need to worry about your own publication record, particularly for a young researcher, the answer isn't so clear. Of course it depends on many factors including your belief that you or others could extend the work as well as when the next conference deadline occurs.

Oddly enough before the internet (in the eighties) such decisions were easier. You could write up a technical report to establish your result and you would have months before your work spread throughout the community. This gives you plenty of time to try and extend the work. The quick spread of information not only improves collaborative work as it does, but forces us to make decisions that we could avoid in the past.

Small Circuits

Fix a constant k. In 1982 Ravi Kannan showed that some Σ₂^p∩Π₂^p language must not have n^k-size (nonuniform) circuits. Here is a proof sketch: A simple counting argument shows there is a function that depends only on the first 5k log n inputs that is not equivalent to a n^k-size circuit. Just by writing out the quantifiers in Σ₄^p you can compute the lexicographically first such function. Now we have two cases:

1. If SAT does not have polynomial-size circuits then SAT then Σ₂^p∩Π₂^p which contains SAT does not have n^k-size circuits.
2. If SAT has polynomial-size circuits then Σ₄^p=Σ₂^p∩Π₂^p (Karp-Lipton) and thus Σ₂^p∩Π₂^p does not have n^k-size circuits.

This is a wonderful example of a non-constructive proof and giving an explicit Σ₂^p∩Π₂^p language without quadratic-size circuits is open. With better known collapses we can improve the result from Σ₂^p∩Π₂^p to S₂^p.

Vinod Variyam recently observed that the class PP which is not known to contain S₂^p also cannot have n^k-size circuits. Here is his proof: If PP has n^k-size circuits then PP is in P/poly which implies the polynomial-time hierarchy and in particular Σ₂^p is in MA which is in PP which has n^k-size circuits contradicting Kannan.

Read Variyam's paper for details and references.

Larry Stockmeyer

We lost a great complexity theorist over the weekend. From Phokion Kolaitis:

It is with great sadness that I write to inform you that Larry Stockmeyer passed away. He died at his home as he had wished when he fell terminally ill a few weeks ago.

Larry was one of the pioneers of computational complexity who made fundamental and lasting contributions to the field. His death creates a void in our community that cannot be filled.

Indeed Stockmeyer developed many of the important early concepts in complexity such as alternation and the polynomial-time hierarchy, concepts that have laid the foundation for many important works in computational complexity. He had a number of great results throughout his career in complexity and nearly all areas of theoretical computer science. Our community has lost one of its giants.

Strangers in the Same Place

Professor X and Professor Y from the same university attend the same conference. At the end of the conference, Professor X says in a surprised tone "That's the most time I have talked with Professor Y all year." He shouldn't be surprised; this is a story I've heard over and over again (and have even told myself).

A professor's life has many responsibilities. Teaching and research of course but also paper writing, grant proposals, meeting with students, and administrative tasks including seemingly endless committee meetings. When I visit another university I leave most of these responsibilities behind so I can focus on research. I also expect the people who invited me to make time in their schedules so we can work together. That way even a short visit can be quite productive.

As the length of the visit increases it becomes harder to avoid these other responsibilities and the amount of research time per day decreases. In the extreme, two people who work at the same university for years end up spending very little time talking research together.

This explains why teleconferencing will never replace traveling no matter how technologically advanced. The social requirements of a short visit require people to spend time together in ways a teleconference cannot. What teleconferencing will do is "allow" me to attend those endless committee meetings wherever I am.

Journal Rankings

An assistant professor writes

In case you need a topic for your weblog: what about journal rankings for theoretical computer science journals? I was looking for something like that for my tenure portfolio. The only web-info I found on the topic was here whose reliability is hard to judge.

Thanks, I am always looking for topics. Journal rankings do not have as strong a perceived ranking in computer science due to the import we give to conferences. Nevertheless, deans like to classify journal articles in computer science like they do for other fields and ask for a ranking.

Here's how I rank theory journals.

1. Journal of the ACM.
2. SIAM Journal on Computing.
3. A large equivalence class of every other major theory journal.
4. Information Processing Letters which publishes short articles that don't merit publication in the above.

Any ordering of journal consistent with this list is okay though even here we have considerable fluctuation. In most theory journals the editor-in-chief rarely overrules the associate editors recommendations and thus have about the same average acceptance criteria. JACM has the tightest quality controls but still occasionally publishes some weaker papers and quite a few mediocre papers appear in SICOMP though I still rate it higher than the rest.

Special issues rank higher, especially those devoted to the best papers of a strong conference. On the other hand, I put no faith on the quality of theory papers that appear in non-theory and especially non-CS journals no matter how they are ranked in their respective field. More than a few rather weak CS papers have appeared in Science, the gold standard for many other scientific disciplines.

NSF Budget

The US House Appropriations committee has passed the NSF budget at a 2% ($111 Million) cut. There are still many more phases in the budget process to go but this cannot be viewed as good news for science. For various reasons, the NSF is lumped in the same budgetary group as Veteran's Affairs and the veterans lobby better than scientists.

The American Institute of Physics has a detailed report and perspective. Here also is a statement from the Coalition for National Science Funding and some comments from the Computing Research Policy Blog.

Favorite Theorems: Superlinear Bounds on Branching Programs

June Edition

Branching programs give us a nice way to model time and space bounds for Boolean functions in a simple non-uniform model. A branching program is a directed acyclic graph where every non-leaf node is labeled by a variable and has two edges labeled One and Zero. All of the leaves are labeled Accept or Reject. Given an input, one follows a path taking the One edge on a node labeled i if the ith input bit is one and the Zero edge otherwise.

The depth (length of the longest path) of the branching program represents time and log of the size represents space. Lower bounds on branching programs give us lower bounds on unrestricted computation.

In 1999, Miklós Ajtai gave the first polynomial-time computable Boolean function for which any subexponential-size deterministic branching program requires superlinear length.

A Non-Linear Time Lower Bound for Boolean Branching Programs by Miklós Ajtai In other words there exists a specified easily computable function that cannot be solved in linear-time unless one uses nearly linear space.

Ajtai creates a function based on quadratic forms and builds on techniques used in his slightly earlier paper.

For more details I recommend the paper Time-space tradeoff lower bounds for randomized computation of decision problems by Beame, Saks, Sun and Vee which gives a nice history of the problem and the techniques to solve it and generalizes Ajtai's work to the probabilistic setting.

Carl Smith 1950-2004

Maryland Professor Carl Smith passed away last night losing his year and a half battle with brain cancer. He was an expert in inductive inference and an active member of the computational learning community. He traveled extensively making many connections in Holland, Germany, Japan and especially Latvia where he is a foreign member of the Latvian Academy of Science.

Carl Smith also played an important role in the computational complexity community. He organized conferences in the early 80's at Perdue and Maryland on Recursion Theoretic Aspects of Computer Science, precursors to the current IEEE Conference on Computational Complexity. He also co-organized the third Complexity (then called Structures) conference in Georgetown in 1988.

Carl was a colleague and a good friend. We both had sabbaticals in Amsterdam in 1996-7, wrote some papers together and often visited each other afterwards. We shared a love of beer and baseball; I would plan my trips to Maryland around the Orioles home schedule.

I always enjoyed the time I spent with Carl and the many interesting discussions we've had. I, my family, and the entire theory community will miss him greatly.

Extracting Randomness

In this post I will describe some recent results in extracting randomness in terms of Kolmogorov complexity since I (and some others) find Kolmogorov complexity more intuitive than entropy. If you would like a background in Kolmogorov complexity, here are some notes from a short course I taught a few years ago. I have not verified that the Kolmogorov results listed below actually follow from the extractor results but it should be straightforward.

Let K(x) be the smallest program generating x. We say a string x is random if K(x)≥|x|. For this post we ignore O(log n) additive factors to avoid various coding issues.

The optimal extractor paper of Lu, Reingold, Vadhan and Wigderson gives us the following. Let n=|x| and K(x)≥k. For all α>0, there is a polynomial-time computable f such that f(x) outputs a polynomial list of strings of length (1-α)k such that most of these strings are random. Using probabilistic constructions of extractors, if one only requires f to be computable, we can set α=0 for k≤n/2.

Barak, Impagliazzo and Wigderson have a new result (mentioned here) on extracting randomness from independent sources. For any constant δ>0, there exists a k polynomial in 1/δ and a polynomial-time computable f such that if we have x₁,…,x_k with

1. |x_i|=n for all i,
2. K(x_i)≥δn for all i, and
3. K(x₁x₂…x_k)=K(x₁)+K(x₂)+…+K(x_k) (the x_i's are independent)

then f(x₁…x_k) is a random string of length n.

Even more recently Barak, Kindler, Shaltiel, Sudakov and Wigderson have even a stronger result in this direction (mentioned here). For any constant δ>0, there exists a ε>0 and a polynomial-time computable f such that if we have x₁,…,x₇ with

1. |x_i|=n for all i,
2. K(x_i)≥δn for all i, and
3. K(x₁x₂…x₇)=K(x₁)+K(x₂)+…+K(x₇) (the x_i's are independent)

then f(x₁…x₇) is a random string of length εn.

Some Links and Random Thoughts

Michael Nielsen is in the midst of a long series of posts on Principles of Effective Research. Much of what he says seems obvious but the obvious often needs to be pointed out. Update 7/27: Complete Principles now available.

Nielsen mentions a new Erdös number eBay auction. We shouldn't use eBay to get people to pay us to do our research; that's what we have graduate students for.

A couple of computational geometers Suresh Venkatasubramanian and Jeff Erickson have been quite active on their weblogs. Check them out.

Finally for some music to prove theorems by, the BBC has put the entire Beethoven sonata cycle with Portuguese pianist Artur Pizarro online.

Why are CS Conferences so Important?

In nearly every scientific discipline conferences play a minor role. Most conferences have a few plenary speakers mixed with massive parallel sessions where nearly everyone who wants to present can present. The vetting of papers occurs in journals and the quality of one's research is measured much by which journal the work appears.

Computer science conferences are much more selective and the quality of one's work is measured by which conference the work appears. Journals play a far lesser role and many important papers never appear in a journal at all. Why is computer science different?

The answer is technological, namely airplanes. Before air travel conferences were much more difficult to attend and drew from a much more regional audience. Those who made the great effort and time to attend a conference were allowed to present. But presenting your paper at such a conference would not reach the majority of your colleagues. Journals were the most efficient way to broadly publicize your research and took on the more important role and have kept that role for historical reasons.

Computer science started as a field during the jet age. Many more people from a wider geographical base could attend a conference. One could now widely disseminate their research through conferences well before a paper appeared in a journal. Journals still played an important role for refereeing, editing and archiving but never held the importance in computer science as conferences do.

Since then we've seen another technological revolution and the internet easily trumps conferences for quickly distributing your results. Perhaps some new scientific field starting today would have a different internet-based system for judging research. But conferences will remain the primary focus for computer science as journals do for the older scientific disciplines.

Time and Space Hierarchies

What the world needs are the time and space hierarchies clearly spelled out in one place.

A function t is time-constructible if there is a Turing machine M such that on input 1ⁿ outputs 1^t(n) in time O(t(n)). Space constructible functions are defined similarly. All the natural functions are time and space constructible.

DTIME(t(n)) are the set of problems computable by a multi-tape Turing machine in deterministic time O(t(n)) on inputs of length n. NTIME (nondeterministic time), DSPACE and NSPACE are defined similarly.

Let t₁ and t₂ be time-constructible functions and s₁ and s₂ space-constructible function. We let "⊂" denote strict subset. A function f(n)=o(g(n)) if lim_n→∞f(n)/g(n)=0.

1. If t₁(n)log t₁(n)=o(t₂(n)) then DTIME(t₁(n))⊂DTIME(t₂(n)).
2. If t₁(n+1)=o(t₂(n)) then NTIME(t₁(n))⊂NTIME(t₂(n)).
3. If s₁(n)=o(s₂(n)) then DSPACE(s₁(n))⊂DSPACE(s₂(n)).
4. If s₁(n)=o(s₂(n)) then NSPACE(s₁(n))⊂NSPACE(s₂(n)).

The DSPACE hierarchy is straightforward diagonalization. For DTIME the proof is similar but we lose log t₁(n) in the simulation of a k-tape machine by a 2-tape machine.

Straightforward diagonalization does not work directly for nondeterministic computation because one need to negate the answer. For NSPACE we easily get around this problem by using Immerman-Szelepcsényi.

The NTIME hierarchy has the most interesting proof that leads to requiring the "+1" in t₁(n+1). This can make a big difference for t₁(n) larger than 2ⁿ².

An NTIME hierarchy was first proved by Cook and in the strongest form by Seiferas, Fischer and Meyer. We sketch a simple proof due to Zàk.

Let M₁,… be an enumeration of nondeterministic Turing machines. We define a nondeterministic machine M that acts as follows on input w=1ⁱ01^m01^k:

• If k<m^t₁(m) then simulate M_i on input 1ⁱ01^m01^k+1 for t₂(|w|) steps.
• If k=m^t₁(m) then accept if 1ⁱ01^m0 rejects which we can do quickly as a function of the current input size.

This machine uses time O(t₂(n)). If NTIME(t₁(n))=NTIME(t₂(n)) then there is an equivalent machine M_i using time O(t₁(n)).

Since t₁(n+1)=o(t₂(n)) we have for sufficiently large m,

1ⁱ01^m0 in L(M) ⇔ 1ⁱ01^m01 in L(M) ⇔ … ⇔ 1ⁱ01^m01^mt₁(m) in L(M) ⇔ 1ⁱ01^m0 not in L(M) a contradiction.

Bringing Families to Conferences

When we have a conference or a workshop in a tourist location, like Banff, many of the participants bring their non-computer scientist spouses and sometimes their whole families. I rarely do so. The main purpose in attending conferences and workshops is not the talks but to meet with your fellow researchers. The main purpose of a family vacation is to spend time with the family. These conflicting goals would make me feel guilty during the whole conference no matter how I split my time. Sometimes I will bring the wife or the family a week before or after or between conferences but conference time is science time.

Still I cannot fault my fellow scientists who bring their families to conferences. I would much rather they attend the conference with their families than not come at all. Every professional has a major challenge in balancing family and work life and they need to find the right mix that works for them.

Final Notes from Banff

Some final notes from the Banff workshop. First a few lemmas used in Wigderson's talk.

Lemma 1: Let G=(V,E) with n vertices and m edges and m≥4n. Let cr(G) be the number of edge crossings in any planer layout of G. Then cr(G)≥m³/64n².

Lemma 2 (Trotter-Szemérdi): Suppose we have a set of points P and lines L in the plane. Let n=|P| and m=|L|. Let I be the number of indices, i.e. the number of pairs (p,l) with p in P, l in L and line l contains the point p. Then |I| ≤ 4((mn)^2/3+m+n).

Guy Kindler talked about a brand new set of results with Barak, Shaltiel, Sudakov and Wigderson. Among other things they improve on the Barak-Impagliazzo-Wigderson result I mentioned earlier by showing that for any constant δ>0, one can take seven independent sources of n bits each with δn min-entropy and combine them to get O(δn) bits of randomness.

Mario Szegedy talked about his recent work showing that the quantum hitting time of a symmetric ergodic Markov chains is the square root of the classical hitting time, a result that becomes a powerful tool in developing quantum algorithms.

Update 7/12: Group Photo now online.

RESULTAPHOBIA!

A Guest Post by Bill Gasarch and Brian Postow

In the 1970's there was some hope that deep techniques from Computability theory might crack P vs NP. Some nice results came out of this (e.g., Ladner's theorem that if P ≠ NP then there is a set inbetween). Then the oracle results seemed to say these techniques (whatever that means) would not work.

In the 1980's there was some hope that deep techniques from Combinatorics might crack P vs NP. Some nice results came out of this (e.g., PARITY not in AC₀, and the monotone circuits lower bounds). Then the Natural Proofs framework seemed to say these techniques (whatever that means) would not work.

So where are we now? Fortnow and Homer's paper on the History of Complexity Theory seems to say that we have no ideas at this time. A recent talk at Complexity seemed to say "we didn't work on this aspect of the problem since, if we solved it, we would have P ≠ NP."

We as a community seemed to be afraid of big separation results. We are almost scared of working on hard problems since they might not pan out. Is this wise? There are stories (some apocryphal some not) about people solving problems because they didn't know they were hard. (Examples below)

I recognize that working on problems with little hope of success is dangerous. But to shy away from a line of research BECAUSE it may lead to a big result seems... odd.

EXAMPLE ONE: Neil Immerman tells a story about Robert Szelepcsényi. Szelepcsényi's result that Context Sensitive Languages are closed under complement was announced in an issue of EATCS (in the same issue, two other articles mentioned Immerman's own proof that NSPACE is closed under complement, an effectively equivalent result). Szelepcsényi was an undergrad at the time, and his adviser gave him the famous problem as a challenge, probably not really expecting him to actually solve it. He did solve it, perhaps because he was never told that it was an old open problem that others had failed to solve.

EXAMPLE TWO: A prominent researcher (who told me about this, so its verified) was working on Σ₂-SPACE(n) = Π₂SPACE(n) but stopped since it might lead to the absurd result that Σ₁-SPACE(n)=Π₁=SPACE(n).

DEBUNKING: There is a RUMOR that Umesh Vazarani would have had Quantum factoring in P but didn't get it since it was obviously false. He has denied this. (I put this in so that someone doesn't post a comment about it.)

Are there more cases of either people solving a problem because they didn't know it was open OR of people NOT working on a problem because they thought it was hard (and it wasn't that hard)? I'm sure there there are. If you know of any that have been verified please post to comments or email to gasarch@cs.umd.edu and postow@acm.org.

Gems of Additive Number Theory

Yesterday Avi Wigderson gave a talk entitled Gems of Additive/Combinatorial Number Theory where he presented three interesting results about the sizes of sets when you add all the possible numbers from one set with another.

Let A and B be subsets of an Abelian group G and define A+B = {a+b | a in A and B in B}. We define AxB as the same with multiplication when we work over a field. Let |A|=|B|=m.

1. Erdös-Szemerédi: Let A be a subset of the reals. Either |A+A|≥m^5/4 or |AxA|≥m^5/4.
2. Ruzsa: For all k, if |A+B|≤km then |A+A|≤k²m.
3. Gowers: Let E be a set of pairs (a,b) with a in A and b in B. Let A+_EB be the set of values a+b with (a,b) in E. For any δ and k, if |E|≥δm² and |A+_EB|≤km then there is an A'⊆A and B'⊆B with |A'|,|B'|≥δ²m and |A'+B'|≤mk³/δ⁵.

Later Russell Impagliazzo showed how to use finite field versions of these results in his upcoming FOCS paper with Barak and Wigderson. They show how to convert poly(1/δ) independent sources of distributions with δn min entropy to n nearly uniform random bits.

Howdy from Banff

Another fourth of July out of the states, this time at the Banff International Research Station (BIRS), a Canadian mathematical conference center similar in spirit to Oberwolfach and Dagstuhl. BIRS is hosting a workshop on Advances in Complexity Theory with a pretty impressive collection of researchers.

Today's talks focused on PCPs and their applications. Guy Kindler gave an interesting presentation on his work with Khot, Mossel and O'Donnell showing that under a few believable assumptions, the Goemans-Williamson Max-Cut approximation is optimal.

Took some time off to see Greece win Euro2004. Sorry Luis.

JCSS To Pay Editors, Possibly Referees

The Elsevier owned Journal of Computer and System Sciences will pay an honorarium of $100 to a cognizant editor for each paper handled. According to Editor-in-Chief Ed Blum the intent "is to establish the practice of compensating editors for their scholarly contribution to scientific publication and is a partial response to the complaint that we scholars do all the work and the publishers reap all the rewards. This practice will apply to Guest Editors of Special Issues. I am aware that it does not address the problem of journal pricing. I am still working on that. I am pretty sure that we can also give a $50, honorarium to referees, but am awaiting a final OK [from Elsevier] on that." (Thanks to Bill Gasarch for this information.)

Update 8/7/04: JCSS is rescinding this new policy of awarding honoraria for papers handled.