In that light, I was pleased to see from the list of speakers, titles, and (especially) abstracts that this upcoming workshop on the theme appears like it will take a more nuanced approach.

I wish I could go, actually, but the timing (right at the beginning of the semester) is terrible.

Overall I was fairly pleased with how the complexity course I taught this past semester went. Still, there are are few things I would change, or at least that I would like to change, the next time I teach it.

What would I add?

At the beginning of the semester, I had planned to cover more material. There are of course several topics I could add, but what struck me the most looking back over the course was that, with one exception, I didn’t cover a single result from after 1995. Somehow that seems wrong, and I’d like to fix it. Any suggestions for what new(er) results to add? My personal constraints are: (1) it should be a topic that is (relatively) easy to motivate for students from outside TCS, and (2) it should be something where I can cover the full proof, or at least a full proof of the main components, in some “reasonable” number of lectures, conditioned on the other material I already cover. (I don’t like presenting “high-level overviews” of results, which is why I wouldn’t cover Williams’s recent ACC0 lower bound, for example.)

As far as my personal interests go, I would probably spend more time on time- and space-bounded derandomization (including Reingold’s result that SL=L), and possibly average-case complexity. Perhaps I could cover Dinur’s proof of the PCP theorem. I had also planned to cover the (old!) proof that TIME(t) is contained in SPACE(t/log t), and may finally get to that next time.

The only other (minor) thing I would add is a proof of oblivious TM simulation. I didn’t cover it this time around because I didn’t think the result was worth the tedious details of the proof. But oblivious simulation seems necessary (or at least highly beneficial) for several other results, and important enough in its own right, that I think I will add it next time.

What would I cut?

Unfortunately, for every topic added some other topic must be taken away. (This year, for example, I cut Mahaney’s theorem and didn’t feel any loss.) So what goes?

• For starters, I think some lectures can be compressed: my first three lectures, for example, (where I introduce Turing machines, P, NP, and NP-completeness) could surely be compressed to two, and I probably don’t need two lectures to prove IP=PSPACE.
• I may cut my half-lecture discussion on time-space tradeoffs for SAT. I like the result a lot (and will be sad to see it go), and the fact that there is a relatively simple proof is nice, but somehow I don’t find the proof very illuminating and it seems disconnected from other material.
• As discussed extensively here, I am going to pass on teaching Ladner’s theorem next time. (Though I will still mention the result.) I may cut the discussion of the BGS relativization of P vs. NP, though I consider that result important enough that I would think twice before doing so.
• I’d be ok with losing the lecture on zero knowledge. Cool as zero knowledge is, I consider it a “crypto” topic rather than a “complexity” topic.
• I taught Toda’s theorem for the first time this year, but think I will cut it next time around. For one thing, I was not able to convince myself (or the students) why the result is fundamentally interesting — on the face of it, the theorem just relates two complexity classes that are both much more powerful than P. The only argument I can see in its favor is that it shows the power of #P, but I think one’s intuition already says that #P is pretty powerful, and the proof of Toda’s theorem is way too messy to justify this benefit. (I realize that Toda’s theorem has historical significance, but I don’t think that justifies covering it now.)

Other suggestions?

Standard disclaimer: While the notes themselves are in excellent shape, I did not do much “final polishing” before posting them online. In particular, I am inconsistent with how I handle references and I apologize to anyone who feels their work has been slighted.

Comments (and corrections) on the notes are very welcome!

We also have an ongoing search for a director for our cybersecurity center.

1. It is a famous result.
2. The proof is not very difficult (so it doesn’t take a lot of time to cover); though see below.
3. It is in Chapter 3 of the Arora-Barak book, which I am roughly following.

On the other hand, once I thought about omitting it, I came up with stronger reasons not to cover it:

1. To me it seems like a “so what?” result. So there are languages in NP\P that are not NP-complete…who cares? (It is a natural question, but the result isn’t very satisfying because you get a completely ridiculous language.) I am also unaware of any interesting results that are proved by relying on Ladner’s theorem.
2. I find the proof extremely technical, messy, and un-illuminating.
3. I am not aware of the specific techniques being useful in some other context, certainly not for anything I was planning to teach later on this semester.

It is worth comparing Ladner’s theorem to the two other results in Chapter 3 of Arora-Barak (that I will cover this semester): hierarchy theorems, and the [BGS] result that the P vs. NP question does not relativize. Point-by-point:

1. I think both these results are very important in their own right. Moreover, hierarchy theorems are invoked frequently in proofs of other results. The [BGS] result is interesting as an illustration of being able to rule out a particular approach to solving a problem.
2. The proofs of both these results are somewhat technical, but I find them much cleaner than the proof of Ladner’s theorem. I think they also both have a pretty clear high-level intuition (something I find lacking in the proof of Ladner’s theorem).
3. The techniques used are applicable elsewhere (though not anywhere later in my class). The hierarchy theorems offer a clear demonstration of diagonalization (and, of course, are useful starting points when trying to prove other hierarchy theorems). Oracle separations were in vogue a decade or two ago in complexity, and are still popular (though in a different sense) in cryptography. I could imagine that when starting to work on many complexity questions, even today, a first question would be to ask whether the statement you are trying to prove relativizes.

I guess I’ve managed to convince myself not to cover it this semester. Anyone want to try to convince me otherwise?

Conference version: 2005
Submitted to journal: 2008
Accepted to journal (pending revisions): 2010
Revised version submitted: Feb. 2011
Revised version accepted: June 2011
Final manuscript submitted: September 8, 2011
Publication date: ??
(sigh)

The position is fairly open. In particular, I would encourage applicants who work on more applied aspects of computer/network security in addition to those who work on cryptography. Students in the areas of information theory, game theory, or complexity-theoretic aspects of cryptography will also be considered.

If you are interested, please send me an email with a copy of your CV, a short research statement, and the name of at least one reference.

Unfortunately, the final results are not very scientific. At the beginning of the experiment I tracked my time very carefully, making a record in my timesheet (to the nearest quarter hour) every time I switched tasks. I quickly changed to estimating how much time I spent on various tasks at the end of the day, or sometimes a day or two later. Perhaps the biggest source of error is that I only recorded the time I spent during weekdays “at work” and, for the most part, did not include time spent at nights or weekends working from home. Perhaps I’ll fix this going forward, especially if someone can recommend good software to use…

With the above caveats in mind, how did I send my time? Here’s what my records say:

• I spent about 40% of my time on research, where this includes “actual” research (either with students/collaborators or on my own), writing up results, reading papers, and attending talks. This number is somewhat higher than I thought it would be, actually.
• The time spent per paper varies widely. (Unfortunately, I feel the results here are really unscientific since have a lot of research hours accounted to “other”; presumably, some of that represents work that turned into a paper later on.) I did notice that the second-most time I spent on a paper this year was devoted to preparing a journal version of an old conference paper.
• I spent 11% of my time on grant-related activities. I consider this abnormally high! I submitted a lot of grant proposals this year, something I’m planning to cut down on next year. Besides writing proposals, this category includes things like writing quarterly or annual reports, managing budgets, etc.
• I spent roughly 9% of my time on teaching-related tasks. Note that over the course of an entire year this percentage will be lower, since besides class prep I don’t work on teaching at all over the summer.
• I spent 6% of my time on non-research advising. This includes things related to proof-reading, serving on proposal and defense committees, offering feedback on student presentations, and writing recommendation letters. (Note that this category does not include time spent working with students on research; that time is included in the “research” category, above.)
• I spent 8% of my time on other administrative tasks. The bulk of this was my work as part of the faculty hiring committee this year.
• I spent 10% of my time on email, meetings, and “other”. I think this is actually an underestimate, considering that I have the bad habit (which I am hoping to change) of reading and responding to email almost constantly.
• According to my records, I only spent 4% of my time reviewing papers. I think that is an underestimate, but I would also note that a lot of my committee work over the past 12 months was done before I began tracking my time in February.

One thing I’ve learned from tracking time like this is that my days tend to be very fragmented, with a lot of context switching involved. I suspect I’ll be more productive, and happier, if I can reduce the extent to which that happens.