P vs NP - The most important problem in Computer Science

Know a simple way to solve Sudoku puzzles? If there is, let someone know!

YT:
Hackerdashery #2

Inspired by the Complexity Zoo wiki: https://complexityzoo.uwaterloo.ca/Co...

For more advanced reading, I highly recommend Scott Aaronson's blog, Shtetl-Optimized: http://www.scottaaronson.com/blog/
ChaosEnginesays...

Basically, most people think that P probably isn't equal to NP, but it would be really nice if it was (aside from instantly killing any and all online encryption, that would kinda suck)

MilkmanDansays...

I remember studying algorithm time complexities, where ideally the time complexity of an algorithm is a polynomial function -- like O(n)=n^2, or even O(n)=n^100. Most things that seem really hard at first are exponential, O(n)=2^n or whatever. *IF* somebody gets a brilliant stroke of inspiration, those exponential time complexity algorithms sometimes get tweaked to become logarithmic, like O(n)=log(n).

But almost never does a problem that seems really hard at first (exponential) get some brilliant solution that makes it jump into easy (polynomial).

I think we get so caught up in the abstract concepts and semantics that we tend to overlook what seems like common sense: some problems are simply harder than others, with no "magic bullet" solution. So, I think that P is almost certainly NOT equal to NP. But that quote around the 10 minute mark puts that in a pretty eloquent way that is easy to understand even to the layman -- a trait which is entirely too uncommon in academia.

BUT, I must admit that the few occasions when I studied an algorithm that seemed like it obviously couldn't get any better than exponential time complexity, only to be shown a brilliant outside-the-box solution that brought it down to logarithmic time complexity definitely taught me some humility. So, you never know.

Baristansays...

Had a math teacher who thought it was funny to mix in two of these millennium prize problems into a test. It brought some students to tears as they thought they were going to fail. A few of us recognized what they were, but most were still pulling out their hair at the end of the period. The teacher's justification was, it would teach us how to identify problems that could not be solved. Unfortunately more than one student was still trying to solve the first MPP and left the remaining 80% of the test blank.

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