Thursday, March 21, 2019

Back at Dagstuhl

Participants and Their Research Interests

This week I'm in Germany for the Dagstuhl workshop on Computational Complexity of Discrete Problems well timed for Georgia Tech spring break. No Bill, so no typecast, no family, just a bunch of fellow theorists. New this year, beer.

Dagstuhl always had bottled beer (and wine), after all this is Germany. However, Ronen Shaltiel is living his lifelong dream of bringing a keg to Dagstuhl. Turns out Dagstuhl had a refrigerator/tap for a beer keg, one only needs to order and pay for the beer. Ronen's daughter designed a special logo, though the keg contains Bitburger, a fine German pilsner. Prost to Ronen and thanks for the beer.


Of course the fun is hanging with colleagues old and new. Talking about open problems old and new. Used to solve more of them back in the day, now it seems harder.

I did learn a new old theorem, planarity testing, whether you can embed a given graph in the plane so no two edges cross, is computable in log space. In 2000 Eric Allender and Meena Mahajan showed that you can test for planarity in symmetric log space, basically the complexity class whose complete problem is undirected connectivity. In 2005, Omer Reingold famously showed that undirected connectivity is computable in log-space. Thus planarity testing is in log-space, a result you might have missed if you didn't know both papers.

This came out in Eric's talk on his work with Archit Chauhan, Samir Datta and Anish Mukherjee showing that checked whether there is a directed path from a given node s to a given node t in planar graphs can be computed by concurrent-read exclusive-write on parallel random-access machines in logarithmic time, and thus likely weaker than directed s-t paths on general graphs.

Sunday, March 17, 2019

Third Poll on P vs NP and related Questions is out now! And the winner is Harambe!


I took a poll of the theory community (and others) about P vs NP and related issues in 2002, 2012, and 2019 (sorry its not an arithmetic  sequence --- read the third poll article to see why). The 2002 and 2012 polls are on the web (see here and here ), and now the third poll is out and its here or here . All three appear in Lane's Complexity Column in SIGACT News.

I'll give some highlights and thought about the third poll, but for more read the article. Or read all three and see how opinions have changed over time.

0) How many respondents: 100 the first time, and 152 the second time, 124 the third time.

1) P≠NP is at about 80%. When restricted to people who have thought about the problem a lot (my judgement) then it goes to 99%. The strongest P≠NP is by Lance who says

                                People who think P=NP are like people who believe Elvis is alive.

I disagree. I think Elvis is alive and is trying to prove P=NP.

2) When will it be solved? 66% thought it would be solved before 2100, a bit more than in prior years. But also more thought it would never be solved. Some commented that a computer might solve it.  I doubt that, but I do think this poll will be done by a computer in 10 years.

3) Because I used Survey monkey (1) each question got more answers, and (2) most  questions got a forced YES or NO  so less funny comments or room for creative answers. People could still leave comments, and some did.

4) Related to point (3): The last time I did the poll P=BPP was thought by everyone who answered the question. This year far more people answered it and quite a few thought P≠BPP. This may be because Survey monkey had a psychological affect of making people vote even if they didn't really know (people who have thought a lot about P vs NP  all thought P=BPP). Has  there been evidence that P≠BPP that I am unaware of? Or since there has not been that much progress on it maybe they are unequal. 10 years ago I would have thought we would have L=RL by now.

5) The last time I did the poll 10 people thought factoring IS in P and the NSA or the KGB knows that. This time around nobody thought that. Why? Those 10 people have vanished mysteriously.

6) Five people thought P vs NP will be resolved by Harambe. That is more than any person got.

7)  Is this poll worth doing? I would say yes (gee, I have to having done his poll three times) because it is good to have an objective record of subjective opinion.

8) I'll give some of my answers: P≠NP, Elvis is dead, and both will be proven in the year 2525. For more about the future see this.

Thursday, March 14, 2019

Captain Einstein

If the president of the United States uses "complexity" in a tweet, I can't leave it alone.

I got my MIT degree in Applied Mathematics so I don't count, but I know plenty of MIT computer scientists and the one undeniable truth is that I don't want any of them flying my plane.

I also agree with the Donald that a complex environment can often lead to confusion, especially in an emergency. HCI matters.

But that's where it stops. Better technology in the plane and on the ground, combined with better procedures have all but eliminated deadly major commercial airplane crashes in the US and quite rare in the world at large. I'll call that more than a "little gain". I remember the "old and simpler" days where we had deadly airline crashes every few months. No thanks.

I've had great discussions with some of the aerospace engineering professors at Georgia Tech. The amount of effort to get the "front-of-the-plane" software right via formal methods and rigorous testings has become harder to engineer than the plane itself. The "back-of-the-plane" software that controls the video screens and WiFi gets less attention. I can live with safety over movies.

When technology makes things much safer, whether it be planes or self-driving cars, the rare accidents become far more noticeable. while we should use these opportunities to learn and make things safer, the rare accidents help us realize just how much more safer technology can make us.

Sunday, March 10, 2019

Richard Karp: His influence and how to honor him

When I first saw the definition of NP-Complete I first thought if there are NP-complete problems I suspect they are contrived. When I saw the proof that  SAT is NP-complete I thought okay, so there is one natural problem  NP-complete by a trick of encoding, but I suspect there aren't any more.  I then read Karp's article that had 22 NP-complete problems. I thought okay, there are 22, but I suspect there are no more. No I didn't think that. But the point is that Cook and Karp together birthed modern complexity theory by introduction NP-completeness and showing that there are MANY natural problems that are NP-complete.

How many people has Richard Karp inspired? I don't know but I suspect it's a  cardinal between countable and the reals so it may depend on your model of set theory. Later in this post I will present Samir Khuller's story of how Richard Karp inspired him.

How to honor him?  The Simons inst. is currently welcoming contributions to the Richard M Karp Fund, which honors the scientific contributions of Founding Director Dick Karp. The fund will provide vital support for the mission and activities of the Simons institute. They have a deadline of Pi-Day. You can go here to contribute and/or here for a letter from Shafi Goldwasser, Prabhakar Raghavan, and Umesh Vazirani about the fund.

OKAY, Samir's story:

Mentoring and Influence via a Train Journey...

Almost to the day, 33 years ago I was running from my dorm room to catch an unreliable bus to the train station as I headed home for a mid-semester break.  On the way,I  stopped by the mailroom, and not knowing where to put the CACM that had just arrived,  stuffed it into the side of my bag and in the process, dropping my   notebook in the process. On the train, when I looked for my  notebook to go over  some material I realized it was missing! All I had was a CACM and a very long train ride. Skimming through the journal, I found Karp’s Turing Award article “Combinatorics, Complexity, and Randomness“. I  started reading this article, and was riveted! It was one of those life changing moments for me, when my immediate future became clear - I wanted to study Theoretical Computer Science and specifically the complexity of combinatorial problems. Without ever having met Dick Karp, he changed my life forever.

I met Dick long after he influenced me via his Turing Award Lecture and it was a real privilege to have had the opportunity to interview him via a fireside chat at Simons. See here.

I am delighted about the fund Bill mentions above as the money that goes to it will help inspire others as Karp inspired me.





Friday, March 08, 2019

QED

Via Scott, John Horgan wrote a blog post following on his 1993 Scientific American article The Death of Proof. The article talked about computer-generated proofs, experimental mathematics and even mentioned some of our work on transparent proofs (basically time-efficient probabilistically checkable proofs). I got (sarcastically I think) accused of killing mathematics after that article but of course we had traditional proofs about probabilistically check proofs. Andrew Wiles got a sidebar titled "A Splendid Anachronism?" for merely solving the most famous open problem in all of mathematics. Somehow traditional mathematical proofs survived the article.

Meanwhile in CACM, Moshe Vardi writes Lost in Math? 
TCS is surely blessed with mathematical beauty. As a graduate student a long time ago, it was mathematical beauty that attracted me to TCS, and continued to lead my research for many years. I find computational complexity theory (or complexity theory, for short), with its theorems (for example, the time-hierarchy and space-hierarchy theorems) and its open questions (for example, P vs NP), to be hauntingly beautiful. Beauty, yes; but what about truth?
Here here on the beauty of complexity. So what about truth? I cover much of this in my P v NP survey. In short the P v NP captures the most critical aspects of what is efficiently computable but it is not the endpoint. Nevertheless P v NP captures both truth and beauty and that's why the problem has so captivated and guided me throughout my research career.

Monday, March 04, 2019

How are there 20 copies of my new book through other booksellers and why are they so highly priced

(This is about my book PROBLEMS WITH A POINT: exploring Math and computer science
by Gasarch and Kruskal, here. This post is NOT a plug.)

I often see weird pricing on amazon but don't have enough inside information to explain it. This time I have seen some weird pricing on amazon but DO have enough information to be truly baffled.

My book is on amazon. You can buy it

Softcover new: $38.00

Hardcover new: $68.00

Okay, that all makes sense.

OR you can buy it from some other source.

There are 10 copies of the softcover, they claim new,  ranging from $38.00 to $57.00.

There are 2 copies of the softcover, they claim used (how used could it be?), $49 and $53

There are 9 copies of the hardcover, they claim new, ranging from $68.00 to $91.00

There are 2 copies of the hardcover, they claim used, $84.00 and $88.00

This raises two questions

1) I have a copy, Clyde got a copy, and two copy's were send to reviewers. Neither Clyde nor I have sold our copy. So how did 20 or so copies get out there?

2) Why do they cost MORE than list price.

I've asked around and got some answers, but I INVITE you to give more possible answers. If your answer is not just speculation (e.g., `I used to be in the black market  book business and here's the real scoop') then that would be great; however, I will take specuation

POSSIBLE EXPLANATIONS FOR HOW SOMEONE GOT COPIES

1) Clyde and I haven't gotten our free copies yet. Hijacked?  Here's hoping the hijackers read it and enjoyed it before posting it. However, this theory is unlikely since I inquired with World Scientific (our publisher) and found out we'll be getting our free copies in 2 weeks. So this theory will either be confirmed or denied in 2 weeks. I would bet against OR those are some really bad hijackers.

2) Complete ripoff. You pay the money and get NOTHING. I think this was more likely in the early days of amazon (or e-bay or....) but now things are pretty well monitored. I have sold books on amazon and am very impressed with how foolproof it is. Still --- could be.

3) Someone hacked my computer. Really? Where did they get the orange covers? Why would they bother? This is not Harry Potter. Plus I asked our staff and NO this could not happen.

4) Some of the shipment dates are fairly far in the future, so they plan to get an order, then
order the book, and have it send to the buyer, at a profit. Seems like too much sugar for a satoshi, BUT could be profitable if its a bot and its automated to do this with lots of books.

5) My publisher also send the book to other sellers. That does not explain the higher prices.

WHY THE HIGHER PRICES?

1) They are counting on people assuming that other sellers are cheaper without checking. Would people do that? People still fall for the Nigerian billionaire scam, so maybe yes.

2) The seller themselves, which is possibly an army of bots, didn't bother checking but priced it
similar to other books. This is plausible since $38.00 is fairly cheap, so looking at similar books may get you a higher price.

-----
Any speculation is welcome so long as it does not involve space aliens or astrology.


Thursday, February 28, 2019

Flying Pigs Unsafe at Any Speed

Take a moment and imagine a flying pig. Do you see a pig with tiny wings lazily guiding along. But pigs are not particularly slow animals as anyone has seen a pig race at a county fair can attest to that. So why not in the air shouldn't a pig go faster than an unladen African swallow?

I have a point discussing the fastness of a flying pig. Consider my favorite flying pig, P = NP. I would put more probability on an actual flying pig (thanks CRISPR) than polynomial-time algorithms for traveling salesman.

Sometimes I get in the following conversation:

AI person: The P v NP problem is irrelevant as we have machine learning and SAT solvers and we can for all practical purposes solve NP-complete problems.
Me: If P = NP we can solve AI!
AI: If P = NP it's likely to have a very slow poly-time algorithm with high exponents and constants and be for all practical purposes useless.

Let's break that down. The claim is E(running time of SAT|running time of SAT is poly) = cnk for some large c and k. First of all you are conditioning on a probability zero event. Beyond that nearly all the known problems we know that sit in polynomial time have practical efficient solutions. So under the assumption that SAT is one of these problems, why shouldn't the same rule apply. You've already made the assumption we can reduce its running time from exponential to polynomial, so why would it stop at some high polynomial?

If we are going to talk about the hypothetical flying pig P = NP world, let my algorithms run fast.

Tuesday, February 26, 2019

Problems with a Point: Exploring Math and Computer Science


As you can see from Lance's tweet


               Problems with a Point: Exploring Math and Computer Science
               by Gasarch and Kruskal

(ADDED LATER- the World scientific website has more info than amazon and has a table of contents, so here it is: here)

is now available! The tweet says its $68.00 but that's hardcover- paperback is $38.00 (are covers that expensive) and if you like your books already broken in, there are some used copies for $89.00. Makes sense to me (no it doesn't!). Could be the topic of a blog post (probably already was).

Okay, so whats in the book?  One of my favorite types of blog posts is when I make a point ABOUT math and then do some math to underscore that point.  I went through all of my blogs (all? No, I doubt I did that) and picked out blogs of that type. With Clyde's help we EXPANDED and POLISHED and GOT THE MATH RIGHT (in some cases I didn't have any math so we had to supply it).

When I first got a copy (about a month ago) I just couldn't stop reading it. I really like it! This is a non-trivial remark -- often authors get tired of their book, or after a while and wonder things like ``why did I write 300 page on the muffin problem? What was I thinking?'' So the fact that I am very pleased with it is not obvious. Does it mean you will?

If you ever thought `I wish bill would clean up his posts spelling and grammar AND expand on the math AND make it a more cohesive whole' then buy the book!

I will in future posts describe more about writing the book, but this is probably my last post where I plug the book.

bill g.