151–156 of 156 posts
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"because so many have tried, and none succeeded" Words worth of a politician, but not a hacker!
No words worthy of a Hacker - we are bound by reality. Politicians are not.
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To pick on a small part of your comment: Do any theoretical computer scientists seriously worry that a proof that P=NP would threaten cryptography? It's not like a proof would suddenly make an i7 able to factor huge numbers in polynomial time. Also, while all polynomial-time algorithms are considered "tractable" in theoretical CS, that doesn't mean that they're all practical on current hardware (nor does it claim to…
>Do any theoretical computer scientists seriously worry that a proof that P=NP would threaten cryptography? Yeah, that's how crypto works as a field. As soon as there's a shadow of a doubt that something is secure in even the least likely edge case, it gets tossed out. MD5 was basically considered dead once someone showed to how create a collision with (correct me if I'm wrong) two very long, very unlikely, very simi…
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Which randomness models in particular? The two Erdős–Rényi models G(n,p) vs G(n, M)? I thought for almost all purposes they gave the same answer as long as equivalent M and p were chosen in the large n limit, because the concentration around M will be so tight due to the law of large numbers. Is there some other model you're looking at? Random without qualification is used to mean "uniformly". For this specific case…
My sense is that there are hard 3-coloring problems in graphs that don't look "random". Certainly the ones I generate have a small number of vertices with very high degree, and the others are more reasonable. This is why I say that there are potentially things happening with different random models. But you are certainly right on all counts. However, where you say this: .... it's been given "physicist proofs". There'…
Earlier quoted context omitted.
To pick on a small part of your comment: Do any theoretical computer scientists seriously worry that a proof that P=NP would threaten cryptography? It's not like a proof would suddenly make an i7 able to factor huge numbers in polynomial time. Also, while all polynomial-time algorithms are considered "tractable" in theoretical CS, that doesn't mean that they're all practical on current hardware (nor does it claim to…
Factoring is in NP. Proving that P=NP would, by definition, imply that large numbers can be factored in polynomial time. The issue of whether it's a feasible amount of work is exactly what I was addressing.