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What's All This About P ≠ NP?

What's All This About P ≠ NP?. Ken Clarkson Ron Fagin Ryan Williams. IBM Research – Almaden. Does P = NP? Or, P vs. NP. A mathematical issue, not a legal one A million dollar problem Most everyone thinks P ≠ NP the problem is to prove it On August 6, Vinay Deolalikar proposed a proof.

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What's All This About P ≠ NP?

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  1. What's All This About P ≠ NP? Ken Clarkson Ron Fagin Ryan Williams IBM Research – Almaden

  2. Does P = NP? Or, P vs. NP A mathematical issue, not a legal one A million dollar problem Most everyone thinks P ≠ NP the problem is to prove it On August 6, Vinay Deolalikar proposed a proof

  3. Taking this proposed proof seriously People claim proofs all the time, but: D. is a Principal Research Scientistat HP Steve Cook said “This appears to be a relatively serious claim...” Dick Lipton said “...this is a serious effort...” Moshe Vardi said “This looks like a serious paper...” However: it doesn't look like the proof goes through

  4. Finding flaws can take time Four-color Theorem Proven 1879 (Kempe) Bug found 1890 (Heawood) Hilbert's 21st problem Solved 1908 Counterexample 1990 Hilbert's 16th problem, special case Proven 1923 Gaps 1980 Proven 1991

  5. Internet time August 6: Manuscript is sent to 22 people, including Ron Fagin, and put on webpage 7: Blog post (Greg Baker) 8: Slashdot 9: Wikipedia article about D. 10: Wiki for technical discussion established About 340 edits since Fields Medalists are involved And, first version of paper removed 15: Commemorative blogpost: The P≠NP “Proof” Is One Week Old

  6. Updates in internet time First draft, Aug 6 Overwritten several times, removed Aug 17 Second draft Aug 9 to Aug 10 Draft 2 + ε, Aug 9 to Aug 11 Third draft, Aug 11 to Aug 17 Three-page synopsis, Aug 13 Only current public version

  7. Local relevance We have some local experts. In particular: Ron Fagin Founder of Finite Model Theory FMT is a work in mathematical logic Impact on database queries, combinatorics, complexity Ryan Williams [IBM Raviv Fellow] has been very active in the on-line discussions And in particular, gave a convincing counter-argument to one part of the proposed proof

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