Computational Complexity

Wednesday, August 27, 2003

 
Electronic Commerce

Posted by Lance

The call for papers for the 2004 ACM Conference on Electronic Commerce is now available. I'm posting this note as my duty as a program committee member to spread the word of the conference.

Why would an electronic commerce conference want me, a complexity theorist, as a PC member? Electronic commerce has many surprising connections to computational complexity. Consider complex auction situations where different buyers wish to purchase different items with varying needs for combinations of these auctions. One needs to design such auctions which decisions made by the buyers, as well as determining the winner must be computationally efficient. This in addition to the usual needs of auctions to be revenue generating, robust against players trying to cheat the system and other notions of "fairness."

In a more philosophical sense, what is a large financial market but some sort of massive parallel computation device that takes pieces of information and produces prices for securities. How can we model and analyze this process? Computational complexity should play a major role in understanding this model of computing and allow us to develop more efficient financial markets.

8:21 PM #

Monday, August 25, 2003

 
Hello Chicago

Posted by Lance

Here I am, my first day back on the campus of the University of Chicago. It's quiet here, Chicago is on the quarter system and classes don't start here until September 29.

I was on the road during the August 22 anniversary of my first post on this weblog. I hope you have enjoyed reading it this year as much as I have had fun writing it.

2:35 PM #

Wednesday, August 13, 2003

 
Goodbye New Jersey

Posted by Lance

My office is all packed up and ready to be shipped. On Friday we move out of our house. I've moved my web pages to Chicago. Burned my files to CD's. It is disconcerting to see all my life's work (papers, talks, programs, grant proposals, editorial and conference stuff, course material, etc.) fit so easily on one CD-ROM. Uncompressed.

Moving is always sad. I've made many good friends at NEC, in and out of theory. But with change comes the excitement of the new chapter of my life ahead of me.

With being on the road and settling in, posting on this site will be quite sketchy over the next several weeks. But don't worry, as one California gubernatorial candidate would put it, I'll be back.

12:57 PM #

Friday, August 08, 2003

 
A New-To-Me Pumping Lemma for Regular Languages

Posted by Lance

I have a gap in my knowledge of work in theory done between 1979 (the publication of Hopcroft and Ullman) and 1985 (when I started graduate school). So every now and then I see a new result from this time that I should have known years ago. Here is an example from the Winter 1982 SIGACT News, a variation of the regular language pumping lemma due to Donald Stanat and Stephen Weiss.

Theorem: If L is regular then there is a positive integer n such that for every string x of length at least n, there are strings u, v and w with v nonempty such that x=uvw and for all strings r and t and integers k≥0, rut is in L if and only if ruv^kt is in L.

What surprises me about this result is that w does not appear in the conclusion and that the initial r could put the finite automaton in any state before it gets to u. Here is a sketch of the proof.

Let s be the number of states of a finite automaton accepting L. Let y_i be the first i bits of x. For any initial state a, y_i will map it to some state b. So one can consider y_i as a function mapping states to states. There are at most s^s such functions so if |x|≥s^s there is an i and a j, i<j such that y_i and y_j represent the same function. We let u=x₁...x_i-1 and v=x_i...x_j-1. The rest follows like the usual pumping lemma.

Using a result of Jaffe, Stanat and Weiss show that this condition is not only necessary but also sufficient to characterize the regular languages.

9:24 AM #

Wednesday, August 06, 2003

 
Splitting Sets

Posted by Lance

Can every infinite set in P be partitioned into two infinite subsets, each also in P? Uwe Schöning answers this question in the affirmative in the Winter 1982 SIGACT News.

Let's generalize the question by saying that a set A splits a set B if both A∩B and A∩B are infinite. Schöning really shows the more general result that any infinite recursive set can be split by a polynomial-time computable set.

Playing with this splitting notion yields lots of potential homework questions. Try these:

1. Show that every infinite regular language can be split by another regular language. Can every infinite context-free language be split by a regular language?
2. Show there is an infinite recursive set that cannot be split by any regular language.
3. Prove Schöning's result above: Every infinite recursive set can be split by a set in P.
4. For a real challenge, show that there is an infinite co-r.e. set that cannot be split by any r.e. set.

In recursion theory, sets that cannot be split by r.e. sets are called cohesive, and r.e. sets whose complements are cohesive are called maximal. For question 4 you are showing that maximal sets exist, a result first proven by Friedberg in 1958.

7:59 AM #

Monday, August 04, 2003

 
SIGACT News and The Cold War

Posted by Lance

Cleaning out my office I came across some old SIGACT News that Bill Gear had given me when he cleaned out his office after his retirement. The Winter 1982 edition is quite interesting. I was a freshman in college that year, well before I was part of the theory community.

There are some interesting technical articles that I will get to in future posts. But the first two pages were letters to the editor that are chilling reminders of the cold war during that time.

On page two was the following short note from Witold Lipski, Jr. and Antoni Mazurkiewicz from the Polish Academy of Sciences.

We are very sorry to inform you that due to the situation in Poland we do not see any chance to organize our 1982 Conference on Mathematical Foundations of Computer Science.

MFCS started in 1972 as an annual conference rotating between Poland and Czechoslovakia, and now between Poland, Slovakia and the Czech Republic. There was no conferences in 1982 or 1983 and the conference did not return to Poland until 1989.

Talking about the Czechs, there was a much longer letter on page one from James Thatcher of IBM. Here are some excerpts.

On a recent trip to Europe, I visited Prague and had the pleasure of talking with Dr. Ivan M. Havel who is a friend and colleague of many years. Ivan Havel received his Ph.D. in CS from Berkeley in 1971. He joined the Institute for Applied Computer Technology in Prague in 1972 and then in 1974 became a member of the Czechoslovakian Academy of Sciences, in the Institute of Information Theory and Automation.

Ivan's brother, Vaclav Havel, an internationally known playwright, was imprisoned in 1979 for four and a half years for his activities in connection with the Charter 1977 movement.

In 1980, possibly related to his refusal to denounce his brother, Ivan Havel was removed from his position in the Academy of Sciences and was unemployed for several months. Last May, he and Vaclav's wife were arrested and charged with "subversion" for allegedly "collecting and distributing written material oriented against the socialist state and social establishment, with hostile intentions." After four days detention, they were released.

He is employed as a programmer-analyst by META, a home-worker program for the handicapped.

Ivan Havel remained a programmer until after the Velvet Revolution in 1989. After some political work in 1990, he became a docent (associate professor) at Charles University and director of the Center for Theoretical Study where he remains today.

His brother Vaclav went on to become president of the Czech Republic.

3:24 PM #

Friday, August 01, 2003

 
My Life in Email

Posted by Lance

When I move back to Chicago, I will go back to my old email address . I got to thinking about how my career can be described by my email addresses.

As an undergrad at Cornell, I spent several years working for computer services writing an email system in assembly language for the IBM 370. The system was scrapped shortly after I left for grad school at Berkeley. After a year at Berkeley, I followed by advisor, Michael Sipser, to MIT.

I had email addresses at Cornell and Berkeley but I have long since forgotten them. At MIT I wanted the userid "lance", but the name was taken by Lance Glasser, then an MIT professor. So my email became .

When I graduated and went to Chicago, I decided to stick with the userid "fortnow" for an email of . This bucked the trend at the time of having first names for email at Chicago so I had to have aliased to . When the university started system wide email I got though also works.

When I did a sabbatical in Amsterdam my email became or simply . When I moved to the NEC Research Institute my email because aliased to and when the NEC Research Institute became NEC Laboratories America I got my current email .

In addition to this, the ACM has created permanent email addresses, permanent as long as you are an ACM member and I did create an address though I never did give it out (until now). My brother and I now own the domain fortnow.com and I have what I do call my permanent address, . I also am the default receiver for fortnow.com mail, which means that addresses like , or even will all go to me.

All of the email addresses in this post still work and forward to me. But I will stick to using two main email addresses, for work related email and for non-work emails.

I used javascript to generate the emails in this post to avoid adding even more to my heavy spam load. We'll see if it works or whether I start getting spam sent to .

1:11 PM #

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