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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
Taking this proposed proof seriously
People claim proofs all the time, but:
• D. is a Principal Research Scientist at 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
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
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
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
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 counterargument to one part of the proposed proof