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A Tighter Grip on Circuit Depth

May 8, 2015


The polynomial hierarchy is infinite for a random oracle

RossmanServedioTan

Benjamin Rossman, Rocco Servedio, and Li-Yang Tan have made a breakthrough in proving lower bounds on constant-depth circuits. It came from a bi-coastal collaboration of Rossman visiting the Berkeley Simons Institute from Japan and Tan visiting from Berkeley to Servedio at Columbia University in New York. Their new paper solves several 20- and 30-year old open problems.

Today we congratulate them on their achievement and describe part of how their new result works.
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Transcomputational Problems

April 30, 2015


Problems beyond brute force search

Bremermann
Cropped from Wikipedia source

Hans-Joachim Bremermann was a mathematician and biophysicist. He is famous for a limit on computation, Bremermann’s limit, which is the maximum computational speed of a self-contained system in the material universe.

Today Ken and I wish to talk about the limit and why it is not a limit.
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The Anti-Pigeonhole Conjecture

April 26, 2015


A conjecture about faculty behavior

rdkibzwang
“Dr. Kibzwang” source

Colin Potts is Vice Provost for Undergraduate Education at Georgia Tech. His job includes being a member of the President’s Cabinet—our president, not the real one—and he is charged with academic policies and changes to such policies. He is also a College of Computing colleague and fellow chess fan.

Today I want to state a conjecture about the behavior of faculty that arose when Tech tried to change a policy.
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Case Against Cases

April 22, 2015


How to avoid too many cases at least some of the time

Unknown

Theon of Alexandria was history’s main editor of Euclid’s Elements.

Today I want to talk about case analysis proofs.
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Kinds of Continuity

April 15, 2015


Congratulations to John Nash and Louis Nirenberg on the 2015 Abel Prize

NashNirenberg
Combined from src1, src2.

John Nash and Louis Nirenberg have jointly won the 2015 Abel Prize for their work on partial differential equations (PDEs). They did not write any joint papers, but Nirenberg evidently got Nash excited about David Hilbert’s 19th problem during Nash’s frequent visits to New York University’s Courant Institute in the mid-1950s. Nash in return stimulated Nirenberg by his verbal approach of barraging a problem with off-kilter ideas. The Norwegian Academy of Sciences and Letters recognized their ‘great influence on each other’ in its prize announcement.

Today we congratulate both men on their joint achievement.
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A Quantum Two-Finger Exercise

April 8, 2015


More mileage than expected from a little example

CarrollBlackboard
Cropped from World Science Festival source

Sean Carroll is a cosmologist in the Department of Physics at Caltech. He also maintains a blog, “Preposterous Universe,” and writes books promoting the public understanding of science. I have recently been enjoying his 2010 book From Eternity to Here: The Quest for the Ultimate Theory of Time.

Today—yes, Carroll would agree that there is a today—I would like to share an interpretation of a little quantum computing example that occurred to me while reading his book.
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April Fool

April 1, 2015


Non-jokes on April Fool’s Day

nunspriest
Nun’s Priest’s Tale source

Faadosly Polir is the older brother of Lofa Polir. You may recall he invented new ways to apply powerful mathematical techniques to prove trivial theorems, and she once claimed a great result on integer factoring. We have heard from both since, but they haven’t given us any new April Fool’s Day material, mainly because they weren’t fooling to begin with.

Today Ken and I wished to help you enjoy April Fool’s day.
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