Monday, December 31, 2018

Complexity Year in Review 2018

Result of the year goes to
Oracle Separation of BQP and PH by Ran Raz and Avishay Tal
which we wrote about in June. This work solves one of the original open questions in quantum complexity using tools from both quantum and classical circuit complexity. How often do we see oracle results with popular articles in Quanta (ignore the hyperbolic title), The Hindu and CACM?

Runner up goes to the solution of the 2-to-2 Games Conjecture by Subhash Khot, Dor Minzer and Muli Safra early in 2018. Boaz Barak gave a nice two post overview.

In last year's review we talked about the magical breakthroughs of machine learning. This year we seemed to have moved beyond the magic to where machine learning has become a thing. We see the immense value of data and continue to struggle with the ethical challenges of collecting and acting on data, dominance of the big tech companies, training all these students who want to gain expertise in the area and trying to understand why ML works as well as it does. 

The big X-factor is China. Will competition with China spur science literacy and funding in the US like the cold war with the Soviets did? Or will isolation with China limit scientific collaboration like the cold war with the Soviets did? 

The big tech surprise was the rise of electric scooters. Georgia Tech has embraced them and it is a quick way to get around campus.

Some of the other questions I asked last year didn't have interesting answers: What will the Internet look like post-net neutrality? (too early to tell) How will the new tax code play out? (too early to tell) Where will Amazon put HQ2? (New York and DC--only surprise was picking two cities) What can quantum computers with 50 qbits accomplish? (still a good question) Will bitcoin move to $300K or 30 cents? (it dropped but still has real value)

Thanks to our guest posters Vijay VaziraniSamir Khuller and Robert Kleinberg, and anonymous.


We end the year with craziness, the stock market is going through wild gyrations, we have a partial government shutdown including all of NSF and an uncertain political landscape with different parties leading the two houses of congress. We're still in the midst of a technological revolution and governments around the world try to figure how to regulate it. I find it hard to predict 2019 but it will not be quiet.

Wednesday, December 26, 2018

Ker-I Ko (1950-2018)

A few weeks ago as Bill and I prepared for our upcoming year in review post, we noted that we hadn't lost any theoretical computer scientists this year, at least none that we were aware of. Unfortunately we didn't make it through all of 2018 unscathed.

Computational complexity theorist Ker-I Ko passed away peacefully from lung failure on December 13. Ker-I Ko spent most of his career at Stonybrook where he had recently retired to take on a professorship at National Chiao Tung University in Taiwan.

I had only had a few brief meetings with Ko but I knew his work quite well. In his best known work, Ko, in a solo paper, created an infinite series of oracles A1, A2, … such that relative to Ak, the polynomial-time hierarchy collapses to exactly the kth level, that is Σk-1 ≠ Σk = Σk+1 = PH. Ko wielded the switching lemma like a scalpel, pulling part the k-1st and kth levels while leaving enough room to encode the k+1st level. He actually gives two sets of oracles, one which collapses PH to PSPACE while collapsing the hierarchy to the kth level and one that separates PH from PSPACE. Even his oracle showing P=NP≠PSPACE wasn't trivial and I used it as an example of a hard to settle complexity question.

Ko, with Tim Long and Ding-Zhu Du, showed that if P ≠ UP if and only if there exist two sets that were one-to-one length-increasing polynomial-time reducible to each other but not polynomial-time isomorphic. This paper played a large role in helping us understand the isomorphism conjecture.

Ko, with Pekka Orponen, Uwe Schöning and Osamu Watanabe, used Kolmogorov complexity to measure the complexity of an instance of a problem. The instance complexity of x in a set A is the smallest program that will correctly answer whether x is in A, and will not give an incorrect answer for any other y in A, though it can answer "I don't know" for y ≠ x.

Ko also had several papers on complexity of real-valued functions and wrote several textbooks and manuscripts. A big loss for all of us in the complexity world.

Sunday, December 16, 2018

Guest post: Join SIGACT!

This is a guest post by Samir Khuller and Robert Kleinberg.

Dear friends,

As our research community continues to grow and thrive, SIGACT membership has not grown apace. We respectfully urge you to join SIGACT! Membership is very cheap (and does not require ACM membership) – only $15 a year – and by joining you will be lending your support to the many activities that SIGACT undertakes on behalf of the theoretical computer science research community. These include:

  • sponsoring STOC and other theory conferences such as SPAA and PODC, as well as co-sponsoring SODA;
  • awards such as the Knuth, Gödel, and Kanellakis Prizes, the SIGACT Distinguished Service Award, and the best student paper awards at STOC and SODA;
  • supporting the Women in Theory workshop;
  • representing the theoretical computer science community to the ACM and beyond.

In addition to these community benefits, membership comes with individual benefits including voting rights in SIGACT elections, reduced rate for membership in EATCS, reduced conference registration rates at SIGACT-sponsored conferences, access to SIGACT News and announcements sent on the SIGACT email list.

SIG membership does not automatically renew when you renew your ACM membership, and we suspect this may be one reason for the decline in SIGACT membership. So the next time you renew your ACM membership, remember to also join SIGACT or renew your SIG membership! Better yet, why wait? If you’re not a SIGACT member, join right now- you can use this link: here

Please do your part to nurture this important resource for our community.

Respectfully,

The SIGACT Executive Committee

Thursday, December 13, 2018

Inverting Onto Functions

Here's an open question that goes back to a 2003 paper  that I wrote with Steve Fenner, John Rogers and Ashish Naik. The conference paper goes back to 1996.

In that paper we discuss two hypothesis we badly called Q and Q' and it still remains open whether the two hypotheses are equivalent.

Q has a number of equivalent definitions, including

  • For all NP machines M that accepting all strings, there is polynomial-time computable function f such that f(x) is an accepting path of M(x) for all x.
  • For every onto honest polynomial-time computable function g there is a polynomial-time computable function f such that f finds an inverse of g, more precisely g(f(g(x))) = g(x) for all x.
  • TFNP is computable in FP.
For lots more equivalences see the paper

Q' is the bit version of Q. For example

  • For all NP machines M that accepting all strings, there is polynomial-time computable function f such that f(x) outputs the first bit of an accepting path of M(x) for all x.
  • For every onto honest polynomial-time computable function g there is a polynomial-time computable function f such that f finds the first bit of an inverse of g, more precisely for all x there is a y such that g(y) = x and f(x) is the first bit of y.
Now Q implies Q', if you can find an accepting path of M(x) you can just read off the first bit. Does Q' imply Q? 

If P = NP you can find solutions using self-reductions. For Q' self-reduction gets stuck because as you start filling in bits you may lose the "onto" promise. 

On the other hand we don't even know any relativized worlds where Q' is true and Q is false. So either prove that Q' implies Q or show a relativized world where Q' is true and Q is false.

How often can I dole out 22-year old open problems that don't require deep complexity to understand. Can't promise what techniques you'll need to solve it.

Monday, December 10, 2018

Super Asymmetry on The Big Bang Theory: How Realistic?

The TV show The Big Bang Theory portrays academia so I am naturally curious how realistic it is. I have posted about this before (see here) in the context of whether actual things they say about physics are true. Today I post about a recent arc where Amy and Sheldon are working on Super asymmetry.


SPOILER ALERT

1) The name: Super Asymmetry. Its not a field but it could be. I assume its about particle physics but I'm not sure they ever say this. A fine name!

2) Amy is a neurobiologist (this was flagged as not being word, but I think it  is) working with Sheldon on a physical theory that I would assume requires hard math.  Physics is hard! So I wonder how realistic this is. Actually, more important than being hard is that you need a lot of background knowledge. So the questions of interest is: Can an amateur still help in a discovery of a new physical theory? This may depend on the definitions of amateur, discovery, new, and physical.  Alone I would doubt it. But with help from Sheldon, I can believe it. Still, making new discoveries in an old field is hard.

3) Amy and Sheldon first had the idea for super asymmetry on their honeymoon. Most married couples have other things to do on their honeymoon. (I did ask my darling to prove the primes were infinite on our wedding day before I married her. She was nervous so couldn't do it, but normally she could. I know a mathematician who made her spouse memorize the definition of a Banach Space before they got married, and recite it to her on their wedding day before they got married.)

4) After they do most of the work they THEN go track down references. This seems stupid but not unrealistic. You can get excited about a theory and work on it at breakneck speed and not want to slow down to check references. But see next point.

5) Sheldon was counting on this for a Nobel Prize. I would think you would check refs before even thinking in those terms.

6) An article in Russian was found that proved the theory could not work. There are a few things wrong with this:

a) The article used the exact same phrase ``Super Asymmetry'' - that seems unlikely.

b) They seemed to not READ the article, just the first page, and then say. DARN, all that work down the tubes.

c) They seemed to not even try to say `OKAY, they did BLAH, we did BLAH BLAH, how do they compare and contrast' (ADDED LATER- I just saw the episode afterwards. They probably DO have something after all. They should have listened to my advice before going into a funk.)

d) If they did all of that work I am sure SOMETHING can be recovered from it.

7) This is not really a post about The Big Bang Theory. I want to know more about your experiences with research: have you worked on a problem and found out it didn't work or was already done, or something like that. And what happened?


Wednesday, December 05, 2018

Remembering George H. W. Bush

Today is the national day of mourning for George Herbert Walker Bush, one of the best presidents for science and computing. He created PCAST, the President's Council of Advisors on Science and Technology. Bush signed the High Performance Computing Act (introduced by Al Gore), that powered computing research and the Internet through the massive growth of the 90's. His administration started the Human Genome Project and the US Global Change Research Program. He appointed the first and so far only African-American NSF Director.

Bush also started the the short-lived Presidential Faculty Fellows program. As a member of the first class of fellows I got invited to a ceremony in the Rose Garden in June of 1992. I didn't actually get to shake hands with President Bush; in that busy election year we had a joint ceremony with some high school award winners and the National Medal of Technology recipients that included Bill Gates and Joseph Woodland, who invented the bar code scanner used at supermarkets. George Bush famously may or may not have been amazed by this technology a few months earlier at a grocers convention and had no issues joking about it when introducing Woodland.

Sipping lemonade on the White House lawn is not an experience one soon forgets. And I guess I haven't twenty-six years later. Thanks President Bush and God speed.


Sunday, December 02, 2018

George HW Bush passed away- some non-partisan math comments

George HW Bush passed away recently. When he was alive there were 5 living ex presidents. Now there are 4. What is the max and min number of ex presidents? This we will answer. What is the prob of having many living ex-presidents?

What is the max number of ex-presidents alive at the same time? List the times this has happened. Your answer should be a list of statements of the following form:

 Shortly after X took office there were Y ex-presidents: Z(1), Z(2), ... , Z(Y).

I leave a little white space in case you want to try to figure it out, though the point of this post is not to quiz you.
















ANSWER: The max number of ex-presidents alive at the
same time is five. This has happened four times.

--------------------------------------------
ONE: In 1861 just after Lincoln took office there were five living ex-presidents:
Martin van Buren (died in 1862), John Tyler (died in 1862), Millard Fillmore (died in 1874), Franklin Pierce (died in 1869), James Buchanan (died in 1868).

Key factors: (1) Between 1836 and 1860 there were no 2-term presidents, (2) Martin van Buren lived a long time after being president.

TWO: In 1993 just after Clinton took office there were five living ex-presidents:
Richard M. Nixon (died in 1994), Gerald Ford (died in 2006), Jimmy Carter (still alive as of Dec 2018), Ronald Reagan (died in 2004), George HW Bush (died in 2018).

Key factors: (1) Nixon, Ford, Carter, Bush Sr were the equivalent of 4 one-terms, and (2) Reagan lived a long time after being president.

THREE: In 2001 just after George W. Bush took office there were five living ex-presidents:
Gerald Ford (died in 2006), Jimmy Carter (still alive as of Dec 2018), Ronald Reagan (died in 2004), George Bush (died in 2018).  Bill Clinton (still alive as of Dec 2018).

Key factors: (1) Ford, Carter, Bush Sr. were effectively 3 one-terms, and (2) Reagan lived a long time after being president.

FOUR: In 2017 just after Donald Trump took office there were five living ex-presidents:
Jimmy Carter (still alive as of Dec 2018), George  HW Bush (died in 2018).  Bill Clinton (still alive as of Dec 2018).  George W Bush (still alive as of Dec 2018).  Barack Obama (still alive as of Dec 2018).

Key factors: (1) Carter, Bush were both one-termers,  (2) Clinton and W are relatively young for presidents and in good health, and  (3) Carter and Bush Sr. lived  a long time (Carter is still living!)

------------------------------------

I want to see this record broken! I want to see 6 living ex presidents! (Darling asks why I want to see that. Its a good question which I will partially address later.) Hence I want to see Donald Trump impeached or resign or leave office!  I was hoping it would would happen before one of Carter, Bush Sr, Clinton, W, Obama died. Oh well.

So now what? Is it possible that we will see 6 living ex-presidents in our lifetime. Factors: prez longevity, prez age, one-term vs two-term, and since I am asking about in OUR lifetime, our longevity.

Lets assume that neither The Donald nor any other president resigns or gets impeached or leaves office before their term is up. We assume that the presidents after Trump are  Alice, Bob, Carol.

Scenarios:

ONE: Donald Trump loses to Alice in 2020, Alice loses to Bob in 2024. None of the ex presidents dies before 2025. Then we would have, in the first day of the Bob presidency, which would be  in  2025,  6 living ex presidents:  Carter, Clinton, W, Obama, Trump, Alice.

This needs Carter to live to be about 100 (the others are much younger). Possible!

TWO: Donald Trump loses  to Alice in 2020, Alice loses to Bob in 2024 . Bob loses to Carol in 2028. Carter passes away before 2025 but the other ex presidents are alive in 2029. Then we would have, in the first day of the Carol presidency, which would be in 2029, 6 living ex presidents:Clinton, W, Obama, Trump, Alice, Bob.


This needs W, Clinton, Trump  to live to be about 83 and Obama to live to be 72.  Possible!

I'll stop here, but you can make up your own SCENARIO THREE which requires some people to live to 87.

Scenario ONE seems unlikely. TWO and THREE are plausible; however, there is another factor. I am assuming a long string of one-termers (that was flagged as not-a-word. Oh well.)  Lately incumbency has a big advantage: Clinton, W, Obama were all two-termers. Incumbency is powerful for two reasons that reinforce each other:

The incumbent can DO things, can LOOK presidential.

Since the incumbent has these advantages people are scared to run against him or her.

--------------------------------------
Math problem: What is the probability that we will see 6 living ex presidents by 2029? To solve this you would need to know

Longevity statistics. But of what group? by Age? by profession? of ex-presidents? That seems to narrow for good statistics.

Incumency statistics. How likely is it for a Prez to be re-elected? Again, too small a sample size. And Trump seems like an outlier. I suspect that if Jeb or Hillary were president they would get re-elected because of the incumbency advantage. But Trump is so unusual that it might not hold. One thing in his favor: it is unlikely there will be a challenge from his own party. One thing in his disfavor would be a third party challenge. But ENOUGH. My point is that it would be hard to do good stats here.

-------------------------------------


So why do I care about seeing 6 living ex-presidents in my lifetime? I have a reason but its not a good reason.

Early in the Nixon Presidency LBJ died. I noticed that there were ZERO living ex-presidents. I knew that LBJ was dead, and JFK was dead, and I suspected (correctly) that Eisenhower and Truman were dead, and I knew FDR was dead. Before that we have Hoover and others who were of course dead. I was SO PROUD of myself for KNOWING this (to be fair I was 12 years old). This sparked my interest in presidents and especially in the question of most/least living ex-prez.

Now for the obvious question on the other end of the spectrum:

What is the min number of ex-presidents alive at the same time? And when did it occur (list all times)

White space for those who want to try to figure it out or look it up.
























ANSWER: Zero. This happened six times.

ONE: When George Washington was president there obviously were zero living ex-presidents.

TWO: Shortly after John Adams became president George Washington died. At that time there were zero ex-presidents.

THREE: During Ulysses S Grant's term Andrew Johnson, the prior president died. Lincoln was dead by assassination and all prior presidents were dead of old age  or similar (e.g., James Buchanan died at the age of 77, Franklin Pierce (an ancestor of Barbara Bush (nee Pierce) was 65 and died of cirrhosis of the liver, from alcoholism.)

FOUR: During Theodore Roosevelt's term Grover Cleveland died, and all other ex-presidents were dead.  Recall that the prior prez, McKinley, had been assassinated.

FIVE: During Herbert Hoover's term, following Calvin Coolidge's death (Hoover's predecessor), there were no ex-presidents.  This partially explains why Coolidge didn't run- he had health problems.  Note that Harding died in office.

SIX: During Nixon's term, in 1973, Lyndon Johnson died. At that time there were zero ex-presidents.  This was because Lyndon Johnson died young (65), Kennedy was assassinated, Eisenhower was old while president.


NOTE: I would have thought that since FDR served so long and died in office either during FDR's term or Harry Truman's term there would be a time with no living ex-presidents.  Early in FDR's term there was only one living ex-president: Hebert Hoover. However, he didn't die until 1964. Hence he lived through the presidencies of FDR, Truman, Eisenhower, Kennedy, and part of Johnson's.  This is NOT the most presidents an ex-president has lived through after they step down. That honor might go to Carter who has lived through the presidencies of Reagan, Bush Sr, Clinton, W, Obama, and, as of this writing, a few years of Trump.  I have not checked if this is a record but I will once Carter passes away.

NOTE: In most of the cases above a recent president had died prematurely. Grant- Lincoln, Roosevelt- McKinley, Hoover- Coolidge, Nixon- Johnson and Kennedy.)

NOT: Since Obama, W, and Clinton are all relatively young, and presidents dying in office is now very rare (the last one was JFK in 1963)   I doubt this will happen again. But politics and history can surprise you.








Wednesday, November 28, 2018

LOGCFL Venkat Style

H. Venkateswaran, a much loved professor in the School of Computer Science at Georgia Tech and a fellow computational complexity theorist, is retiring at the end of December. In honor of Venkat I'd like talk about my favorite paper of his, relating LOGCFL to semi-unbounded circuits.

Let's start with context-free languages. Even if you never took a theoretical computer science course, you probably saw them in elementary school.


A context-free language is a series of rules like S-> NP VP or N->man. The context-free part comes from the fact that a noun phrase (NP) produces the same sentence fragments wherever it appears. CFLs have a rich theory--there have been whole textbooks devoted to the topics.

LOGCFL are the set of problems that are reducible to context-free languages with a small-space reduction. Formally, A is in LOGCFL if there is a CFL B and a log-space computable function f such that for all x, x is in A if and only if f(x) is in B.

Venkat showed that LOGCFLs are equivalent to semi-unbounded circuits, log-depth circuits with unbounded OR gates but bounded AND gates, the class now called SAC1 (technically the equivalence holds for log-space uniform SAC1 but that's not important). His proof goes through various models of alternating Turing machines and push-down automata.

Context-free languages are not closed under complement, for example 0n1n0n is not context-free but its complement is. Somewhat surprisingly Borodin, Cook, Dymond, Ruzzo and Tompa showed that LOGCFL is closed under complement, combining the Immerman-Szelepcsényi inductive counting technique with Venkat's circuit characterization of LOGCFL.

The Borodin result implies that you whether you have bounded ORs and unbounded ANDs, or bounded ANDs and unbounded ORs, you compute the same class.

Enjoy your retirement Venkat. We'll miss you!

Monday, November 26, 2018

If you think a theorem is true then spend half your time trying to prove its true, and half trying to prove its false.

There is a quote I recall but not who said it.  I have not been able to find it on the web.


If you think a theorem is true then spend half of your time trying to prove that its true, and half trying to prove that its false.

I thought it was Erdos but I could not find any connection between him and the saying. I did find something that indicates he did not say it:

An Erdos problem that pays different amounts of money for the conjecture being true of false:

--------------------------------------------------------------------------------
For a finite family F of graphs, let t(n,F) denote the smallest integer m that every graph on n vertices and m edges must contain a member of F as a subgraph.

A problem on Turán numbers for graphs with degree constraints} (proposed by Erdös and Simonovits [1]. $250 for a proof and $100 for a counterexample)

Prove or disprove that
t(n,H)=O(n^{3/2})
t(n,H)=O(n^{3/2})
if and only if H does not contain a subgraph each vertex of which has degree >2

Bibliography
1 P. Erdös, Some of my old and new combinatorial problems, Paths, flows, and VLSI-layout (Bonn, 1988), Algorithms Combin., 9, 35-45, Springer, Berlin, 1990.
----------------------------------------------------------------------------------------

A while back there was a $1,000,000 prize for PROVING Goldbach's conjecture (the prize had a deadline which is past). See here. However, the article does not say what you win for a counterexample. I suspect nothing. Is this fair? (1) YES- proving Goldbach would be hard, where as if its false just finding the counterexample likely won't require hard math, (2) NO- HEY, they resolved it, so there, (3) Have a panel look at the solution and decide if it has merit.

ANYWAY- if someone knows the source of the quote, please let me know.

Tuesday, November 20, 2018

Is Secret sharing REALLY REALLY REALLY used?

Since I am teaching Cryptography this semester I am teaching things people REALLY REALLY REALLY (RRR) use. For some topics this is RRR true, like RSA (that it is used to transmit a private key that is then used is FINE.)

I was wondering if Information-Theoretic Secret Sharing is RRR used. I am asking non-cynically and non-rhetorically. So I want to be taken seriously AND literally.

  I Googled and got some answers but could not verify them.

1) At this site: here we can read

Every modern HSM (hardware secure module, for crypto applications) uses Shamir's secret sharing.

I tried to verify this but was unable to.

I also read

The DNSSEC root key is 5-out-of-7 shared see, e.g., here or here

The link leads to a story about how there are 7 people and if any 5 get together they can shut down the internet. The story does not say they use secret sharing.

2) Threshold cryptography (see here) would seem to use it, but is Threshold crypto used? There is a startup who is trying to use it: see here. I don't count that as RRR since they don't have customers yet. Not sure what the threshold is for whether I count it.

3) Some papers mention that secret sharing COULD be used if you want to make sure nuclear missiles are not launched unless x out of y people say so. But I doubt it really is used. If so this might be very hard to verify.

4) Shamir's secret sharing scheme is pretty simple and does not have big constants so if there is a need it really could be used. But is there a need?

I am not quite sure what I count as proof that someone RRR  using it. A random person at a random website just saying that HSM uses it does not seem convincing. A Wikipedia article saying its being used I would find convincing (should I? Until recently Wikipedia couldn't even get my year of birth straight, see here)

If some companies website said they used Shamir's Secret Sharing I would believe that-- but a companies website is not likely to say that. NOT for reasons of company secrets but because its not what most customers go to the website to find.

SO- if someone RRR knows that Secret Sharing is RRR being used then please leave a comment.

Thursday, November 15, 2018

Simons and Amazon

I'm spending this week at the Simons Institute in smokey Berkeley, California. This fall Simons has a program in Lower Bounds in Computational Complexity. Scroll down that page and you'll see the rather strong collection of participants that are spending much of the fall at the Institute.

I purposely chose a week without a workshop--I'd rather talk to people than sit in talks. My former PhD student Rahul Santhanam is hosting me and we are having some fun discussions about the minimum circuit-size problems, pseudorandom generators and white vs black box algorithms. I've grown a little rusty in complexity during my years as department chair and have to work to keep up with Rahul. The student has become the master.

Even a quiet week at Simons is not that quiet. Every night seems to have a theme: trivia, board games, pub night, music night. I participated in a discussion with the "journalist in residence" on how to make lower bounds interesting to the general public. As part of a Turing awardee lecture series, Andy Yao gave a talk on Game Theory in Auction and Blockchain which included some reminiscing of Yao's golden time in Berkeley back in the early 80's when he helped lay the mathematical foundations of modern cryptography.

Simons started as a competition and, while I was on team Chicago, I have to admit Berkeley has done a wonderful job with the institute. We've just seen the results from another competition, with Amazon splitting their "second headquarters" between Northern Virginia and Queens, missing an awesome opportunity in Atlanta (not that I'm biased). Not surprised about the DC area, but pretty surprised about separating the HQ into two locations, neither planned to reach the level of activity of HQ1 in Seattle. Amazon stated that they didn't think they could find the tech talent to fill 50,000 positions in a single city. So much for "build it and they will come".

Monday, November 12, 2018

And the winner is again, Harambe: A pre election poll of my class that was truly a referenum on the Prez

I had meant to post this before the election but I didn't quite time it right. Oh well.

It has been said that this midterm election (more than others) was a referendum on the prez.  Every prez election year I have my students (or someone's students) vote (Secret Ballot of course) for president. ((see 2016 , 2012, 2008) This year, for the first time, I had a midterm election, though rather than ask them which Maryland people they would vote for, I made it truly a referendum on Trump by asking two questions:

1) Who did you vote for in 2016?

2) Knowing what you know now, who would have have voted for in 2016?

Full Disclosure: I am in the Clinton/Clinton Camp. However, this is an information-post not an opinion-post, so my vote is not relevant nor was it counted.

I give the full results at the end of the post; however, I will summarize the most interesting data: the change-mind people and my thoughts.

4 voted Trump and now wish they voted differently: Harmabe, Clinton, Nobody, Gasarch

Only 12 people had voted for Trump in 2016 and of those 4
regret it. While I can see wanting Clinton, Nobody, or Gasarch,
I'm surprised someone wanted Harmabe. Is he even a citizen?

5 voted Clinton and now wish they voted differently: 2-Johnson, Trump, Kanye, Gasarch.


Since Clinton hasn't done anything to merit rejection since the election,
I deduce these people are more going TOWARDS the one they picked rather
than AWAY from her. Trump has been Prez and has done stuff, so Clinton/Trump
makes sense -- the student's opinion is that Trump is doing better
than expected. Gary Johnson hasn't done anything to merit a change towards
him, so thats a puzzler.  Kanye, similar. As for Gasarch, if the reasoning
is `he's doing a good job teaching crypto, lets make him president' doesn't
really work since he's not doing THAT good a job. If it was Ramsey theory
then I could see it.

Misc:
1 Underwood(House of Cards)/Satan (For those tired of picking the LESSER of two evils)
1 Stein/Clinton
1 Johnson/Clinton
1 Kruskal/Gasarch (some people can't tell them apart)

The two who went to Clinton I interpret as thinking Trump is worse
than expected.

ALSO: Hillary had 28 Hillary/Hillary. Hence Trump had the largest percentage of people who regret voting for him, but still only 1/3. And the numbers are to small to make much of them.

MY OPINON: FORTNOW in 2020!

------------------------------------------------------

61 students did the poll.

-----------------------------
Stayed the same:

-----------------------------
Stayed the same:

28 Clinton/Clinton
8 Trump/Trump
4 Stein/Stein
3 Johnson/Johnson
1 Kasich/Kasich
1 Sanders/Sanders
1 Jerry White/Jerry White (Socialist Party)
1 Bofa/Bofa (this is a joke)
1 Thomas Adam Kirkman/Thomas Adam Kirkman (prez on TV show Designated Survivor)

48 do not regret their vote.

-------------------------
Trump/XXX

1 Trump/Harmabe (Harambe is the Gorilla who got shot in a zoo.)
1 Trump/Clinton
1 Trump/Nobody
1 Trump/Gasarch (Gasarch would prove the problems of government are unsolvable rather than solve them)

FOUR people voted Trump and now regret it.

------------
Clinton/XXX

2 Clinton/Johnson
1 Clinton/Trump
1 Clinton/Kanye
1 Clinton/Gasarch


FIVE people voted Clinton and now regret it.

-------------
MISC changed

1 Underwood(House of Cards)/Satan (For those tired of picking the LESSER of two evils)
1 Stein/Clinton
1 Johnson/Clinton
1 Kruskal/Gasarch (some people can't tell them apart)

TWO people who voted third party now would have voted Clinton.
I interpret this as not-liking-Trump since I don't think Clinton
has done anything since the election to make anyone thing better
or worse of her, while as Trump as president has done enough
to change people's opinions of him.

Thursday, November 08, 2018

The Data Transformation of Universities

With all the news about elections, caravans, shootings and attorney generals, maybe you missed the various stories about real transformations at our top universities.

On October 15 MIT announced the Stephen A. Schwarzman College of Computing. Schwarzmann donated $350 million to the effort as part of an expected billion-dollar commitment that will pay for a new building and fifty new faculty.
“As computing reshapes our world, MIT intends to help make sure it does so for the good of all,” says MIT President L. Rafael Reif. “In keeping with the scope of this challenge, we are reshaping MIT. The MIT Schwarzman College of Computing will constitute both a global center for computing research and education, and an intellectual foundry for powerful new AI tools. Just as important, the College will equip students and researchers in any discipline to use computing and AI to advance their disciplines and vice-versa, as well as to think critically about the human impact of their work. 
Two weeks later the University of California at Berkeley announced a Division of Data Science to be led by an associate provost reporting directly to the provost (like a dean).
“Berkeley’s powerful research engine, coupled with its deep commitment to equity and diversity, creates a strong bedrock from which to build the future foundations of this fast-changing field while ensuring that its applications and impacts serve to benefit society as a whole,” said Paul Alivisatos, executive vice chancellor and provost. “The division’s broad scope and its facilitation of new cross-disciplinary work will uniquely position Berkeley to lead in our data-rich age. It will simultaneously allow a new discipline to emerge and strengthen existing ones.”
Sorry Berkeley, you are anything but unique. Every major research university is trying to build up expertise in computing and data science given the demands of students, industry and researchers across nearly all academic disciplines who need help and guidance in collecting, managing, analyzing and interpreting data.

Here at Georgia Tech, where we've had a College of Computing since 1990, we recently started an Interdisciplinary Research Institute in Data Science and Engineering and a Interdisciplinary Research Center in Machine Learning both to be housed in a twenty-one story CODA building that will open next year in Midtown Atlanta (sounds impressive when I write it down).

I could go on for pages on how other universities are rethinking and transforming themselves. Earlier this year Columbia (who hired Jeannette Wing to run their data science institute) held a summit of academic data science leadership. The report shows we have much to do.

The real secret is that none of us have really figured it out, how to meet the escalating needs for computing and data and integrating it across campus. We aim at a moving target problem as we sit just at the beginning of the data revolution that will reshape society. The future looks rocky, scary and fun.

Monday, November 05, 2018

Is Fuzzy Sets Common Knowledge? How about Napier as inventing (or something) logs?

Darling: Bill, help me with this crossword puzzle. 6 letter word that begins with N, clue is log man

Bill: Napier

Darling: Who was that?

Bill: A famous lumberjack

Darling: Give me a serious answer

Bill: Okay. He is said to have invented logarithms. Like most things in math its not quite clear who gets the credit, but he was involved with logarithms early on.

Darling: I said give me a serious answer. That is rather obscure and would not be in a crossword puzzle.

While darling is wrong about the answer being wrong she is right about it being obscure. How would your typical crossword puzzler know the answer? Perhaps Napier appears in a lot of crosswords since it has lots of vowels, so they just word-associate `log man' to `Napier'  But in any case this does seem odd for a crossword puzzle.

In the quiz show Jeopardy, in round two, the following was an $800 question under philosophy (the questions are 400,800,1200,1600,2000, so 800 is supposed to be easy)

In 1965 Lotfi Zadeh introduced this type of set with no clear boundaries leading to the same type of ``logic''

1) I suspect that all my readers know that the correct response is `Fuzzy' (or formally `What is Fuzzy')

2) Why is this in Philosophy? There IS an entry of it in the Stanford Enc of Phil (see here). Some Philosophers work on Logic, but do they work on Fuzzy Logic? The wikipedia page for Fuzzy Logic (see here) has only one mention of phil and its to the Stanford Enc of Phil chapter.

3) (more my point) Is Fuzzy Logic so well known as to be an easy question on Jeop? See next point

4) Can someone get this one right WITHOUT knowing ever having heard of Fuzzy Logic. I suspect yes and, indeed, the contestant DID get it right and I think she had never heard of Fuzzy Logic. While I can't be sure one tell is that when a contestant says `what is fuzzy logic' and it actually sounds like a question, then they are partially guessing.

Anyway, I am surprised that this obscure bit of math made it into an easy question on Jeop. But since the contestant got it right, it was appropriate.

Thursday, November 01, 2018

P = NP Need Not Give a SAT Algorithm

In Bill's post earlier this week, he asks if there is a fixed algorithm such that if P = NP, this algorithm will correctly compute satisfiability on all inputs. While I believe this statement is true because P ≠ NP, I would like to argue we won't prove it anytime soon.

Bill links to a TCS Stack Exchange answer by Marzio De Biasi giving a fixed algorithm that would get SAT correct except on a finite number of inputs if P = NP. Here is Marzio's algorithm.

Input: x   (boolean formula)
Find the minimum i such that
  1) |M_i| < log(log(|x|))  [ M_1,M_2,... is a standard fixed TM enumeration] 
  2) and  M_i solves SAT correctly 
       on all formulas |y| < log(log(|x|))
          halting in no more than |y|^|M_i| steps
          [ checkable in polynomial time w.r.t. |x| ]
  if such i exists simulate M_i on input x 
      until it stops and accept/reject according to its output
      or until it reaches 2^|x| steps and in this case reject;
  if such i doesn't exist loop for 2^|x| steps and reject.

This proof relativizes: There is a fixed relativizing Turing machine M such that for all A, if PA = NPA then L(MA) runs in polynomial time and differs from SATA on only a finite number of strings. SATA is a relativizable form of SAT with a built in relations that answer whether a sequence of variables encode an string in A. SATA is NPA-complete for all A.

The following shows any proof that a fixed algorithm can compute all of SAT correctly if P = NP cannot relativize.

Theorem: For every deterministic Turing machine M, there is an A such that PA = NPA and either Mdoes not compute SATA correctly on all inputs or Mtakes at least exponential time.

Proof:

Define B = {0x | x in TQBF}. TQBF is the PSPACE-complete problem containing all the true quantified Boolean formula. PTQBF = PSPACE = NPTQBF and thus PB = NPB.

Let φn be the formula that is true if there exists a string z of length n such that 1z is in A. Let n be the smallest n such that MBn) takes less than 2n computational steps. If no such n exists let A = B and we are done.

If MBn) accepts we are done by letting A=B since B has no string beginning with 1.

If MBn) rejects and uses less than 2n steps there must be some z such that MBn) did not query 1z. Let A = B ∪ {1z}.

MAn) still rejects but now φn is in SATA. Also PA = NPA since adding a single string to an oracle won't affect whether two classes collapse.

Monday, October 29, 2018

If P=NP then we HAVE an alg for SAT.

I am writing up the result of my survey of peoples opinion of P vs NP (it will be in a SIGACT News, in Lane's Complexity Column, in 2019.) Some  people wrote:

                          P=NP but the proof will be nonconstructive and have a large constant.

Large constant could happen.

If by nonconstructive they mean not practical, then yes, that could happen.

The following does not quite show it can't happen but it does give one pause:  an old result of Levin's shows that there is a program you could write NOW such that if P=NP then this program decides SAT except for a finite number of formulas (all of which are NOT in SAT) and can be proven to work in poly time (I will later give three pointers to proofs). The finite number of formulas is why the people above may still be right. But only a finite number- seems like a weak kind of nonconstructive.

Since I am teaching crypto I wondered about Factoring. An old result of Gasarch (I proved it this morning -- I am sure it is already known) shows that there is a program you could write NOW such that if Factoring is in P then this program factors a number ALWAYS (none of this finite exception crap) and can be proven to work in poly time. Even so, the algorithm is insane. If someone thought that factoring in P might be nonconstructive, my construction disproves it in such an absurd  way that  the notion that factoring could be in P nonconstructively should be taken seriously but not literally. There should be a way to say formally:

I believe that FACTORING is in P but  any poly-time algorithm is insane (not even looking at the constants) and hence could never be implemented.


Not sure how to define insane.

Three pointers:

Stack Exchange TCS:  here

Wikipedia: here

My slides (also include factoring result): here

Question: Can the SAT result be improved to be an algorithm that is ALWAYS right? Is there a way to show that it can't be (unless, say P=NP).

Question: What can be said about Graph Isomphism in this context? The proof for SAT is easily adpated to this case (all we used about SAT was that it was self-reducible). But can we get our GI algorithm to never make a mistake?

Thursday, October 25, 2018

Good Results Made Meaningless

Sometimes you see a beautiful theorem A that you love to talk about. Then another beautiful theorem B comes around, making the first one meaningless since B trivially implies A. Not just a mere extension of A but B had a completely different proof of something much stronger. People will forget all about A--why bother when you have B? Too bad because A was such a nice breakthrough in its time.

Let me give two examples.

In STOC 1995 Nisan and Ta-Shma showed that Symmetric logspace is closed under complement. Their proof worked quite differently from the 1988 Immerman-Szelepcsenyi nondeterministic logpsace closed under complement construction. Nisan and Ta-Shma created monotone circuits out of undirected graphs and used these monotone circuits to create sorting networks to count the number of connected components of the graph.

Ten years later Omer Reingold showed that symmetric logspace was the same as deterministic logspace making the Nisan-Ta-Shma result an trivial corollary. Reingold's proof used walks on expander graphs and the Nisan-Ta-Shma construction was lost to history.

In the late 80's we had several randomized algorithms for testing primality but they didn't usually give a proof that the number was prime. A nice result of Goldwasser and Kilian gave a way to randomly generate certified primes, primes with proofs of primeness. Adleman and Huang later showed that one can randomly find a proof of primeness for any prime.

In 2002, Agrawal, Kayal and Saxena showed Primes in P, i.e., primes no longer needed a proof of primeness. As Joe Kilian said to me at the time, "there goes my best chance at a Gödel Prize".

Monday, October 22, 2018

Please Don't call them Guidance Counselors

As I mentor many HS students I was recently in email contact with the HS contact for projects and I noticed that the sign off was

Allie Downey
Guidance School Counselor

This piqued my interest so I emailed her asking why the cross out.

She was delighted to answer! Here is her email:

Thank you, but “Guidance Counselor” is an outdated term.  It is from a time before there was the American School Counselor Association, before the profession required at least a  Masters degree, and before there was a nationally recognized comprehensive school counseling program. Guidance is a service; school counseling is a program.  This is a great website that explains it even better here

Thank you for taking the time to ask.  Anyone in the profession today prefers the term School Counselor and I always appreciate when people inquire.

I asked her further about the difference and here is what she said:

Everyone  in a young person’s life offers guidance in some fashion.  School counselors still provide guidance classroom lessons (such as bully prevention and character development), but we do so much more.  We help students develop their academic abilities and study skills.  We assist them and their families in college and career planning.  We teach coping skills so students can guide themselves.  We ask questions to help these young adults discover the answers on their own.  We help students learn how to advocate for themselves.  We console.  We mediate.  We learn and adapt with changing climates.  We work with families, faculty, and community members to make sure school is a safe place for students to learn and grow. And this is all before the lunch bell. It is an amazing profession and I am proud to call myself a school counselor.

Thursday, October 18, 2018

A New Cold War?

Imagine the following not-so-unrealistic scenario: The US-China trade war deepens leading to a cold war. The US blocks all Chinese citizens from graduate school in the US. Visas between the two countries become hard to get. The Chinese close off their Internet to the West.
If things continue along this path, the next decade may see the internet relegated to little more than just another front on the new cold war.
I wouldn't have thought it in our hyperconnected age but we are in spitting distance of going back to the 60's. What would this all mean for science and computing?

Let's go back to the original cold war between the Soviet Union and the US roughly from 1947-1991. We didn't have a significant internet back then (though we can thank the cold war for the internet). One had to assume that the government read mail to/from USSR. Travel to and from the USSR and the Eastern block to the west was difficult. Academic research did cross over but only in dribs and drabs and we saw two almost distinct academic cultures emerge, often with duplication of effort (Cook/Levin, Borodin/Trakhtenbrot, Immerman/Szelepcsényi).

Beyond the limited communication came the lack of collaboration. Science works best with open discussion, sharing of ideas and collaborating with each other. It took a Russian and an American working together to give us Google.

No cold war in this age can completely cut off ideas flowing between countries but it can truly hamper knowledge growth. We can't count on US superiority with China already ahead of us in areas like high-speed trains, renewable energy and mobile payments.

The cold war did have an upside to science: The competition between the East and the West pushed research growth and funding on both sides. We already see arguments for quantum computing and machine learning by the necessity of staying ahead of the Chinese. But science funding should not be driven by fear but by curiosity and its indisputable long-term effects on our economy.

We must keep the flow of information and people open if we want science and technology to flourish to its fullest, from students through senior researchers. Don't let a new cold war bring us back to the days of separate communities, which will fail to produce the breakthroughs we will never know about.

Sunday, October 14, 2018

Practical consequences of RH ?

When it seemed like Riemann Hypothesis (RH) might be solved (see Lipton-Regan blog entry on RH  here and what it points to for more info) I had the following email exchange with Ajeet Gary (not Gary Ajeet, though I will keep his name in mind for when I want to string together names like George Washington, Washington Irving, Irving Berlin,  with the goal of getting back to the beginning) who is an awesome ugrad at UMCP majoring in Math and CS.

Ajeet: So Bill, now that RH has been solved should I take my credit cards off of Amazon?

Bill: I doubt RH has been solved. And I think you are thinking that from RH you can prove that factoring is in P. That is not known and likely not true.

Ajeet: What are my thoughts and why are they wrong?

Bill: What am I a mind-reader?

Ajeet: Aren't you?

Bill: Oh, Yes, you are right, I am. Here is what you are confusing this with and why, even if you were right you would be wrong.

Ajeet: It just isn't my day.

Bill: Any day you are enlightened is your day. Okay, here are the thoughts you have

a) From the Extended RH (a generalization of RH) you can prove that PRIMES are in P. (This algorithm is slow and not used. PRIMES has a fast algorithm in RP that people do use. Primes was eventually proven to be in P anyway, though again that is a slow algorithm). Note- even though we do not know if ERH is true, one could still RUN the algorithm that it depends on. ERH is only used to prove that the algorithm is in P.

b) There was an episode of Numb3rs where they claimed (1) RH implies Factoring in P-- not likely but not absurd (2) from the proof of RH you could get a FAST algorithm for factoring in a few hours (absurd). I say absurd for two reasons: (i) Going from basic research to application takes a long time, and (ii) See next thought

c) If (RH --> factoring easy) then almost surely the proof would present an algorithm (that can be run even if RH has not been proven) and then a proof that RH --> the algorithm's run time is poly. But I wonder -- is it possible that:

RH--> factoring easy, and

The proof does not give you the algorithm, and

 if you had a proof  or RH then you COULD get the algorithm (though not in a few hours).

I doubt this is the case.

Ajeet: So are there any practical consequences of RH?

Bill: Would you call better bounds on the error term of the prime number theory practical.

Ajeet: YES!

Bill: GREAT! For more on RH see here

Thursday, October 11, 2018

2018 Fall Jobs Post

As we do every year at this time, we help you find that perfect academic job. So who's hiring in CS this year? Perhaps we should instead follow the advice of John Regehr.
For computer science faculty positions best to look at the ads from the CRA and the ACM. For theoretical computer science specific postdoc and faculty positions check out TCS Jobs and Theory Announcements. If you have jobs to announce, please post to the above and/or feel free to leave a comment on this post.

Even if you don't see an ad, almost surely your favorite university is looking to hire computer scientists. Check out their website or email someone at the department.

And (selfish plug) Georgia Tech is looking to hire in theory this year.

Some generally good advice: Make sure you have strong letter writers who know your research well, best if one or two of them come from outside your university. Put all your papers and materials on your website and make sure your Google Scholar page is accurate. Put effort into your job talk and remember you need to sell you research to non-theorists. Good if you can connect to other areas especially machine learning, data science or cybersecurity. Quantum seems hot this year.

Above all have fun! In this computational and data driven world we live in, there is a great job out there for you.

Monday, October 08, 2018

A New ACO Center (guest post by Vijay Vazirani)

Guest Post by Vijay Vazirani

                                                          A New ACO Center!

Last week, I helped launch an ACO Center (Algorithms, Combinatorics and Optimization) at my wonderful new home, UC Irvine. There are only two other such centers, at CMU and Georgia Tech (29 and 27 years old, respectively). My personal belief is that there will be more in the future. Let me justify.

When I joined Georgia Tech in 1995, my research was centered around approximation algorithms, a topic that resonated with its ACO Center. I was able to build on this interest in numerous ways:  by offering new versions of courses on this topic as new results emerged, attracting to GT, for the first time, a large number of top theory PhD students who went on to produce stellar results and start impressive careers of their own. Course notes accumulated over the years eventually lead my book on the topic in 2001. Right after that, I switched to algorithmic game theory, and again ACO became the center of that activity, this time resulting in a co-edited book which had a huge impact on the growth of this area. In short, ACO gave me a lot!  In turn, I believed in it and I worked for it wholeheartedly.

I still believe in ACO and I feel it is very much relevant in today’s research world. Similar to the other two ACOs, our Center at UCI also exploits the natural synergies among TCS researchers from the CS Department, probability and combinatorics researchers from the Math Department, and optimization researchers from the Business School. Additionally, our Center has grown well beyond these boundaries to include a highly diverse collection of faculty (e.g., from the prestigious  Institute for Mathematical Behavioral Sciences) whose common agenda is to utilize the “algorithmic way of thinking”, which is set to revolutionize the sciences and engineering over the course of this century, just as mathematics did in the last. The Center website has further details about its vision and activities.

Many universities are in a massive hiring mode today (especially in CS), e.g., UCI  plans to hire 250 new faculty over the next five years. Centers such as ours present the opportunity of hiring in a more meaningful manner around big themes. They can also be instrumental in attracting not only top students but also top faculty.

A center of excellence such as GT’s ACO does not simply spring up by itself; it requires massive planning, hard work, good taste and able leadership. For the last, I will forever be indebted to Robin Thomas for his highly academic, big vision, classy leadership style which was the main reason ACO remained such a high quality program for so long. Moving forward, will we stay with three ACO Centers or will there be more? I believe the latter, but only time will tell.

Saturday, October 06, 2018

John Sidles, Mike Roman, Matt Howell, please email me/hard to get emails of people

John Sidles, Mike Roman, Matt Howell : please email me. at gasarch@cs.umd.edu (my usual email)

I need to ask you about some comments you left on the blog a while back (or emailed me -- I forget which, but I can't find your emails if you did email me). I need you to contact me SOON!

When you do I will tell you whats up and why I decline to say here what this is about.

For my other readers -- it is nothing controversial.


How hard is it to find people's emails on the web?

Sometimes it takes less than 5 minutes

Sometimes it is impossible.

Sometimes I get it by asking someone else who knows, or knows who to ask... etc.

It is rare that more time on the web helps. I do not think I ever spend more than 5 minutes and then found it. I have sometimes used linked-in. I don't have a Facebook account (I was going to put in a link to the latest Facebook privacy breach, but (1) by the time you read this they may have had another one, (2) you all know about it, and (3) when I typed in `Facebook Scandal' to Google I got the Facebook page for the TV show Scandal.)

Should people make their emails public? I can see why one does not want to. The old saying is that if you owe people money you want to be hard to find, but if people owe you money you want to be easy to find.

Contrast email to what people DO put online. A few years ago I needed someone's email address. I found his website. From his website I found out the exact day he lost his virginity. Okay... Didn't need to know that. But I still could not find his email address.  I later asked someone who asked someone etc. and got it. But I was struck by what was private and public. This is NOT a complaint (though I wish it was easier to fine email addresses) just an observation.

Thursday, October 04, 2018

Google added years to my life

If you google

gasarch

you used to  get the following:   here

Please go there and notice how old they say I am.

Okay, you are back. You may have noticed that they say I am 68. Gee, I don't feel 68 (I feel younger).

I have no idea how Google got my age wrong.

0) I found about this when I saw my age in an article about the Muffin problem. The article is here. I had been in contact with the author earlier so it was easy to contact him, assure him that I appreciate his throwing scammers and spammers off of my trail by giving me the wrong age, but I wondered why he chose 68. He then apologized (which was not needed) and pointed me to the google thing.

1) My age was  not on my Wikipedia page. Nor was my birth year.

2) I do not recall every telling Google my age -- but then again, Google knows what I search for and perhaps deduced an incorrect age from that (I've been watching a very old Western, Maverick, lately, which may have fooled them. So my plan is working!)

3) Google thinks I published with Hilbert (see here or here) so that would make them think I am 68 years old. Hmm, still to young. If I was a 10-year old math genius in 1938 (Hilbert died in 1943 but since I am not a 68 year old math genius I chose numbers to make it easy) and published with
him then, then I would now be 80. Not 68. So that is not the answer.
(Side question- are any of Hilbert's co-authors still alive?)

Seriously, if anyone has any ideas why Google had it wrong, let me now

4) Lance was outraged at this and hence put my birth year on my Wikipedia page thinking that
would fix it. (I was not outraged, just amused.)

5) It was taken off my page since Lance couldn't prove it.

6) Lance and I  mentioned my age in a blog post and that was proof enough. So our blog is a primary
source. We should use this sparingly -- with great power comes great responsibility. (See here for more on that theme)

7) Other weird internet stuff: What does it take to get a Wikipedia Page? A Nobel Prize in Physics
helps. See: here.


Monday, October 01, 2018

Muffin Math

Lance: It's Friday afternoon and the Dagstuhl workshop has ended. We have some time before we need take off so how about one final typecast.

Bill: Always a good idea.

Lance: First the exciting news, Nitin Saxena won the Shanti Swarup Bhatnagar prize for 2018,
Nitin Saxena
according to the many Indians at Dagstuhl, the most prestigious science prize in the country. The awards were announced on Wednesday during the workshop. He's the S in AKS.

Bill: That's really impressive. He was only two-years old when AKS had log-depth sorting networks.

Lance: Bill, you moron. You're thinking of Ajtai-Komlós-Szemerédi. I'm talking Agrawal-Kayal-Saxena Primes in P, topic of my second ever blog post. Nitin, an undergrad at that time, didn't just sit on his laurels--he has had awesome results on algebraic circuit complexity that truly justify this prize.

Bill: Well congrats to Nitin. Moving on, let's talk math.

Lance: We're at Dagstuhl so we have to call it computer science.

Bill: Ronen Shaltiel gave a great but depressing talk, Indistinguishability by adaptive procedures with advice, and lower bounds on hardness amplification proofs.

Lance: Nobody sings the Dagstuhl Blues.

Bill: Suppose you had a hard function and want to covert it to a harder function, known in the biz as hardness amplification. For constant depth circuits we have hardness results but no known process for amplification. For larger classes, like constant depth circuits with threshold gates, we do know ways to amplify.

Lance: But we have not hardness results there? Where are you going with this?

Bill: Ronen put it nicely, "We can only amplify hardness where we don't have it". Ronen and his colleagues proved results along those lines. Lance, does that depress you.

Lance: Not as much as the sprained ankle that made me miss that talk. My turn to pick a favorite talk. I loved Michael Forbes Hitting Sets for the Closure of Small Circuits. You take algebraic circuits with a parameter epsilon and take the limit as epsilon goes to zero. Forbes and Amir Shpilka show a PSPACE algorithm to find small sets containing non-zeros of these functions. These kinds of functions are studied in the GCT approach to lower bounds.

Bill: What lower bounds is this aiming to solve?

Lance: Showing the computation difference between the determinant and the permanent.

Josh Alman: You've left out the most exciting part of the conference.

Bill and Lance: So Josh, what was that?

Josh Alman: The world debut debut performance of Stud Muffin and Smilin' Sam singing "Do You Work on Muffin Math?"



Lance: That awesome duo looks familiar Bill. Where I have seen them before?

Bill: That Sam can really tickle the ivories.

Lance: And Stud was definitely in the room.

Bill: On that note, take us out.

Lance: In a complex world, keep it simple.

Thursday, September 27, 2018

Still Typecasting from Dagstuhl

Lance: Bill, in our typecast earlier this week I said you were older than me. But 68? You don't look day over 66.

Bill: Neither do you. But seriously, why do you think I'm 68?

Lance: I just Google'd "How old is Bill Gasarch?"

Bill: Don't believe everything you read on the Internet. I'm really 58.

Lance: Prove it.

Bill: Here's my driver's license.

Lance: Bill you don't drive. And it literally says "NOT A DRIVER'S LICENSE" on the back. But it is an official State of Maryland Identification card stating that you were born in 1959. Are you saying I should trust the state of Maryland over Google?

Bill: Yes, because they pay my salary. Back to Dagstuhl. Let's talk about the talks. William Hoza gave a nice talk about hitting sets for L (deterministic small space) vs RL (randomized small space)  but when I asked him when will we prove L = RL he said not for fifty years. Grad students are not supposed to be that pessimistic.

Lance: You mean realistic. Though I'd guess more like 10-20 years. I wouldn't even be surprised if NL (nondeterministic log space) = L.

Arpita Korwar: I say 10-15 years.

Bill: Can we put that in the blog?

Lance: Too late. Bill I heard you were the stud muffin this week.

Bill: Yes, I talked about the muffin problem. Got a problem with that?

Lance: Needed milk. I saw this talk two years ago and now you have cool theorems. Who would've thought if you have 24 muffins and 11 people you can allocate 24/11 muffins and the smallest piece is 19/44, and that's the best possible for maximizing the smallest piece.

Bill: I can't believe you actually listened to the talk and didn't fall asleep.

Lance: zzzzzz. Did you say something?

Bill: Never mind. Eric Allender talked about the minimum circuit-size problem: Given a truth-table of a function f is there a circuit for f less that a given size w. The problem is frustrated, just consider the following theorem: if MCSP is NP-complete then EXP does not equal ZPP (exponential time in zero-error probabilistic polynomial-time).

Lance: Do you think EXP = ZPP?

Bill: No, the result only tells us it will be hard to prove MSCP is NP-complete without informing us whether or not it is NP-complete. Allender did show that under projections it isn't NP-complete (Editor's Note: I should have said log-time projections see Eric's comment. SAT and all your favorite NP-complete problems are complete under log-time projections). MSCP might be complete under poly-time reductions but not under weaker reductions.

Lance: Reminds me of the Kolmogorov random strings that are hard for the halting for Turing reductions but not under many-one reductions.

Bill: Everything reminds you of the Kolmogorov strings.

Lance: As they should.

Bill: I liked Michal Koucký's talk on Gray codes.

Lance: Shouldn't that be grey codes. We're not in the UK.

Bill: It's the color you moron. It's named after Frank Gray.

Lance: You are smarter than you look, not bad for a 68 year old. I missed Koucký's talk due to a sports injury, but he did catch me up later.

Bill: I never put Lance and sports in the same sentence before.

Lance: And I never put Bill and driving together. It's a new day for everything. Koucký showed how to easily compute the next element in the Gray code querying few bits as long as the alphabet size is of size 3.

Bill: Which contrasts Raskin's 2017 paper that shows with a binary alphabet you need to query at least half the bits.

Lance: Hey you stole my line.

Bill: That's not possible. You are editing this. I think this typecast has gone long enough. Take us out.

Lance: In a complex world, best to keep it simple.

Tuesday, September 25, 2018

Lance and Bill go to Dagstuhl: The Riemann Edition

Lance: Welcome to our typecast directly from Dagstuhl in Southwestern Germany for the 2018 edition of the seminar on Algebraic Methods in Computation Complexity. Say hi Bill.

Bill: Hi Bill. So Lance are you disappointed we didn't go to Heisenberg for the Michael Atiyah talk claiming a solution to the Riemann Hypothesis.

Lance: I knew how fast I was going but I got lost going to Heisenberg. I think you mean the Heidelberg Laureate Forum a 100 miles from here. From what I heard we didn't miss much. For those who care here is the video, some twitter threads and the paper.

Bill: Too bad. When I first heard about the claim I was optimistic because (1) László Babai proved that graph isomorphism is in quasipolynomial-time at the age of 65 and (2) since Atiyah was retired he had all this time to work on it. Imagine Lance if you were retired and didn't have to teach or do administration, could you solve P vs NP? (This gets an LOL from Nutan Limaye)

Lance: I'll be too busy writing the great American novel. Before we leave this topic, don't forget about the rest of the Laureate Forum, loads of great talks from famous mathematicians and computer scientists. Why didn't they invite you Bill?

Bill: They did but I rather be at Dagstuhl with you to hear about lower bounds on matrix multiplication from Josh Alman. Oh, hi Josh I didn't see you there.

Josh: Happy to be here, it's my first Dagstuhl. I'm flying around the world from Boston via China to get here. Though my friends say it's not around the world if you stay in the Northern hemisphere. They are a lot of fun at parties. But not as much fun as matrix multiplication.

Bill: So Josh, what do you have to say about matrix multiplication. Is is quadratic time yet?

Josh: Not yet and we show all the current technique will fail.

Bill: Wouldn't Chris Umans disagree?

Kathryn Fenner: You shouldn't pick on Canadians [Ed note: Josh is from Toronto]. Pick on students from your own country.

Josh: (diplomatically) I think Chris Umans has a broader notion of what counts as known methods. There are some groups that aren't ruled out but we don't know how to use them.

Chris: Very well put. The distinction is between powers of a fixed group versus families of groups like symmetric groups. The later one seems like the best place to look.

Lance: Thanks Chris. Josh, what are your impressions of Dagstuhl so far?

Josh: I like the sun and grass. I wish it was easier to get here.

Lance: This is only the first day. You haven't even found the music room yet, past the white room, past the billiard room where Mr. Green was murdered with the candlestick. Oh hi Fred Green. Luckily Dr. Green is still alive. I remember my first Dagstuhl back in February of 1992.

Josh: Two months before I was born.

Lance: Way to make me feel old.

Bill: You are old.

Lance: You are older. Believe it or not six from that original 1992 meeting are here again this week: The two of us, Eric Allender, Vikaurum Arvind, Uwe Schöning and Jacobo Torán. Amazing how accents show up as we talk.

Bill: What did I sleep through this morning before Josh's talk?

Lance: Amnon Ta-Shma talked about his STOC 2017 best paper and Noga Ron-Zewi showed some new results on constructive list-decoding.

Bill: Let's do this again later in the week. Lance, takes us out.

Lance: In a complex world, best to keep it simple.

Thursday, September 20, 2018

Why wasn't email built securely?

Recently I talked with Ehsan Hoque, one of the authors of the ACM Future of Computing Academy report that suggested "Peer reviewers should require that papers and proposals rigorously consider all reasonable broader impacts, both positive and negative." which I had satirized last May.

Ehsan said that "if email had sender authentication built in from the beginning then we wouldn't have the phishing problems we have today". Leaving aside whether this statement is fully true, why didn't we put sender authentication and encryption in the first email systems?

Email goes back to the 60's but I did get involved on the early side when I wrote an email system for Cornell in the early 80's. So let me take a crack at answering that question.

Of course there are the technical reasons. RSA was invented just a few years earlier and there were no production systems and the digital signatures needed for authentication were just a theory back then. The amount of overhead needed for encryption in time and bandwidth would have stopped email in its tracks back then.

But it's not like we said we wish we could have added encryption to email if we had the resources. BITNET which Cornell used and the ARPANET gateway only connected with other universities, government agencies and maybe some industrial research labs. We generally trusted each other and didn't expect anyone to fake email for the purpose of getting passwords. It's not like these emails could have links to fake login pages. We had no web back then.

But we did all receive an email from a law firm offering green card help. My first spam message. We had a mild panic but little did we guess that spam would nearly take down email at the turn of the century. Nor would we have guessed the solution would come from machine learning which kills nearly all spam and much of the phishing emails today.

I don't disagree with the report that we shouldn't think about the negative broader impacts, but the true impacts negative and positive are nearly impossible to predict. Computer Science works best when we experiment with ideas, get things working and fix problems as they arise. We can't let the fear of the future prevent us from getting there.

Monday, September 17, 2018

What is a Physicist? A Mathematician? A Computer Scientist?

 Scott Aaronson recently won the Tomassoni-Chisesi Prize in Physics (yeah Scott!).
In his post (here) about it he makes a passing comment:

I'm of course not a physicist

I won't disagree (does that mean I agree? Darn Logic!) but it raises the question of how we identify ourselves. How to answer the question:

Is X a Y?

(We will also consider why we care, if we do.)

Some criteria below. Note that I may say thinks like `Dijkstra is obviously a computer scientist'
but this is cheating since my point is that it may be hard to tell these things (though I think he is).

1) If X in a Y-dept then X is a Y. While often true, there are some problems: MIT CS is housed in Mathematics, some people change fields. Readers- if you know someone who is in dept X but really does Y, leave a comment. (CORRECTION- I really don't know how MIT is structured. I do know that the Math Dept has several people who I think of as Computer Scientists: Bonnie Burger,  Michael Goemans, Tom Leighton, Peter Shor, Michael Sipser. There may be others as well. The point being that I would not say `Sipers is a mathematician because he is in the MIT Math Dept')

2) If X got their degree in Y then they are Y. Again, people can change fields. Also, some of the older people in our field got degrees in Physics or Math since there was no CS (I am thinking Dijkstra-Physics, Knuth-Math). Even more recently there are cases. Andrew Child's degree is in Physics, but he did quantum computing. Readers- if you know someone who got there degree in X but is now donig Y, leave a comment.

3) Look at X's motivation. If Donald Knuth does hard math but he does it to better analyze algorithms, then he is a computer scientist. One problem -- some people don't know their own motivations, or it can be hard to tell. And people can get distracted into another field.

4) What does X call himself? Of course people can be wrong. The cranks he email me their proofs that R(5) is 40 (its not) think the are mathematicians. They are not- or are they? see next point

5) What X is interested in, ind. of if they are good at it or even know any. Not quite right- if an 8 year old  Bill Gasarch is interested in the Ketchup problem that does not make him a mathematician.

6) What X is working on right now. Fine but might change. And some work is hard to classify.

7) If you win an award in X, then you are an X. Some exceptions

Scott is a computer scientist who won the Tomassoni-Chisesi Physics Prize

Ed Witten is a Physicist who won the Fields Medal (Math)

John Nash is a mathematician who won a Nobel prize in Economics.

I want to make a full circle- so if you know other X won a prize in Y then leave a comment and
we'll see what kind of graph we get. Bipartite with people on one side and fields on the other.

8) What they can teach? Helpful in terms of hiring when you want to fill teaching needs.

Does any of this matter? We use terms like `mathematician' `physicist' `computer scientist' as shorthand for what someone is working on, so its good to know we have it right.


Thursday, September 13, 2018

P = NP and Cancer

Often when the question comes to what happens if P = NP, one typically hears the response that it kills public-key cryptography. And it does. But that gives the impression that given the choice we would rather not have P = NP. Quite the opposite, P = NP would greatly benefit humanity from solving AI (by finding the smallest circuit consistent with the data) and curing cancer. I've said this before but never explained why.

Of course I don't have a mathematical proof that P = NP cures cancer. Nor would an efficient algorithm for SAT immediately give a cancer cure. But it could work as follows:
  1. We need an appropriately shaped protein that would inhibit the cancer cells for a specific individual without harming the healthy cells. P = NP would help find these shapes perhaps just the DNA of the person and the type of cancer.
  2. At this point we don't understand the process that takes a ACGT protein sequence and describes that shape that it forms. But it must be a simple process because it happens quickly. So we can use P = NP to find a small circuit that describes this process.
  3. Use P = NP to find the protein sequence that the circuit from #2 will output the shape from #1.
We'll need an truly efficient algorithm for NP problems for this to work. A n50 algorithm for SAT won't do the job. All this steps may happen whether or not P = NP but we'll need some new smart algorithmic ideas.

Please note this is just a thought exercise since I strongly believe that P ≠ NP. I do not want to give false hope to those with friends and loved ones with the disease. If you want to cure cancer your first step should not be "Prove P = NP".