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Jumping GI down from the nearly-exponential neighborhood to the nearly-polynomial one László Babai is one of the world experts on complexity theory, especially related to groups and graphs. He also recently won the 2015 ACM Knuth Prize, for which we congratulate him. Today we wish to discuss a new result that he has announced that will place graph isomorphism almost in polynomial time. More exactl
The role of definitions in mathematics and theory Alfonso Bedoya was not a theoretician, but an actor. He is perhaps most famous for uttering the lines: “Badges? We ain’t got no badges. We don’t need no badges. I don’t have to show you any stinking badges!” He played Gold Hat, in the The Treasure of the Sierra Madre. Today I want to talk about definitions. We all think mostly about theorems and pr
Factoring, factoring, the whole day through, keeps on my mind—apologies to Hoagy Carmichael and Stuart Gorrell Michael Rubinstein is an expert on number theory, who is on the faculty of the University of Waterloo. He is one of the organizers of a 61-birthday symposium being held December 15–19 in Princeton for my friend and former colleague, Peter Sarnak. I guess it is a matter of taste for a numb
A principle for checking proofs with an application to the proof Vinay Deolalikar is standing by his claim and proof. He and I have been exchanging e-mails, and as noted in the several comments, he has updated his paper several times. The updates are trying to answer some of the questions raised here and elsewhere. However, the consensus seems to be best summarized by a recent comment here by Tere
Some further comments into the recent claimed proof that P is not equal to NP Yuri Manin is a great mathematician, who has worked in various areas and also is well known for his many excellent expository works. He has won numerous prizes, including the Nemmers Prize in Mathematics in 1994, and the Cantor Medal in 2002. One of his quotes is: A proof only becomes a proof after the social act of “acc
A serious proof that claims to have resolved the P=NP question. Vinay Deolalikar is a Principal Research Scientist at HP Labs who has done important research in various areas of networks. He also has worked on complexity theory, including previous work on infinite versions of the P=NP question. He has just claimed that he has a proof that P is not equal to NP. That’s right: . No infinite version.
Are practical SAT problems easy or hard? Ed Clarke, a Turing Award winner, was at the recent NSF workshop on design automation and theory. Ed has, for approximately three decades, worked successfully on advancing the state of the art of verification, especially that of hardware. Today I want to talk about a discussion that came up at the workshop. Ed and others stated that in “practice” all the in
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