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Possible Issues With the P != NP Proof

Posted by Soulskill on from the intuitively-obvious-to-the-most-casual-observer dept.

An anonymous reader writes "We previously discussed news that Vinay Deolalikar, a Principal Research Scientist at HP Labs, wrote a paper that claimed to prove P is not equal to NP. Dick Lipton, a Professor of Computer Science at Georgia Tech, analyzed the idea of the proof on his blog. In a recent post, he explains that there have been many serious objections raised about the proof. The post summarizes the issues that need to be answered in any subsequent development, and additional concerns are raised in the comment section."

11 of 147 comments (clear)

  1. Incompleteness by im_thatoneguy · · Score: 5, Interesting

    Yes there can be a proof to prove that there is no proof. Check out Godel's Incompleteness Theorem

    http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems

    Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems for mathematics. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The two results are widely interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all of mathematics is impossible, thus giving a negative answer to Hilbert's second problem.

    Not sure if any such effort exists though in this case.

  2. Current Status by pdxp · · Score: 5, Informative

    The paper was preliminary to begin with. It is currently withdrawn in order to fix minor typos and because currently "enough unresolved issues with the paper exist to foster a healthy sense of skepticism". This is a good thing for now.

    The original discussion was in a Google Doc but has since moved to a wiki.

    Info: Previous post explaining the proof more clearly
    Paper (not wort reading for most of us)

    1. Re:Current Status by Affenkopf · · Score: 5, Funny

      The paper was preliminary to begin with. It is currently withdrawn in order to fix minor typos

      Minor typos like a ! that m,ade it into the paper by accident.

  3. Mathematicians are gathering to vet this paper by Xenographic · · Score: 5, Informative

    For anyone interested in the details, you can find a lot more on this wiki, where a lot of mathematicians are weighing in on the proof and its potential flaws. Mathematicians are gathering from all over to examine this paper because it's so interesting. Even if one of the serious objections that have been raised so far kills it, it contains some novel ideas that will get people thinking.

    They've also been gathering the news coverage and such, so it's probably the best place to find up-to-date information about this proof. It seems to have sparked quite a lot of interest for a paper that hasn't even been properly published.

  4. Yes, they've tried that by Xenographic · · Score: 5, Informative

    They've tried that, but all that's been proven so far is that several types of proof won't work, rather than proving that it's impossible to prove. The first few sections of this paper itself go into detail about why this proof isn't one of the kinds of proof that won't work, incidentally.

    Terrence Tao has a blog post on why a P=NP proof can't be relativisable if you're interested. Incidentally, there are several other classes of proof that won't separate P from NP.

    1. Re:Yes, they've tried that by nomoreunusednickname · · Score: 5, Funny

      I have discovered a truly marvelous proof that P!=NP. But this comment is too deterministic to contain it.

  5. I for one by Chuck+Chunder · · Score: 5, Funny

    feel very very stupid after reading that.

    --
    Boffoonery - downloadable Comedy Benefit for Bletchley Park
  6. Publication Bias by mSparks43 · · Score: 5, Funny

    Like I said last time. The trouble is, every time someone proves P=NP, the NSA arranges them a little accident.

  7. Hard core by gregrah · · Score: 5, Interesting

    "Formal Language Theory" - an undergrad course at my university that dealt with Finite State Automata, Touring Machines, Computability Theory, Complexity Theory, and the formal proofs thereof, was the most interesting class that I've ever taken. That being said, I always felt when doing homework for that class that I was taking a dive off the deep end (i.e. pushing the limits of human sanity). And that's only from studying the "low hanging fruit" that people were publishing papers on several decades ago when theoretical computer science was still relatively young. I can't imagine things have gotten any less mind-warpingly complex since then.

    I have tremendous respect for the folks who continue to "dabble" in this stuff. I'm sure that for their efforts they have been rewarded with glimpses of indescribably beautiful works of both man and of nature.

    1. Re:Hard core by tehcyder · · Score: 5, Funny

      "Formal Language Theory" - an undergrad course at my university that dealt with Finite State Automata, Touring Machines, Computability Theory, Complexity Theory,

      How cool was that, I assume it was to give you a theoretical basis for the use of car analogies.

      --
      To have a right to do a thing is not at all the same as to be right in doing it
  8. Re:How? by digitig · · Score: 5, Informative

    Step 3 states that "We cannot accept the definition of the set NP purely in terms of its members having a property (a solution in polynomial time) that we have no reliable mechanism to detect." "Detect" is a bit vague here, but all that's needed for an existence proof (or disproof) is a formal definition, not any means of actually detecting cases. Look at pretty much any proof involving transfinites.

    --
    Quidnam Latine loqui modo coepi?