Re:The polynomial algorithm for 3-SAT problem (or P=NP)
by patio11 on Thursday January 20, 2011 @02:12AM
(#2122967)
The issue of whether it's a feasible amount of work is exactly what I was addressing.
One of the reasons this would be a huge result is that even a very expensive polynomial-time solution for any NP-complete problem (say, one which is O(n^2000) and would take several billion years to run against a 256-bit key) is only going to get faster over time. Also, the experience of cryptography is that once cracks start appearing in an algorithm the mathematicians start trying to wedge their chisels in and hammer those cracks into fractures, into holes, and eventually into whatever you call something which no longer resembles a crack so much it resembles absence-of-wall.
There are specific mechanisms by which this would happen, too. A near miss on P=NP would mean funding for professors looking into refining it, and professional interest generally, would suddenly explode. Nobody wants to fund or work on duds, but big contributions to this problem would make careers.
Not incidentally, while the government funds quite a bit of academic research, this particular branch of mathematics is of special interest to one type of government customer which has ways of getting funding for projects expedited if they are in the national interest... and it is virtually inconceivable that they would not find very, very strong national interest in the vicinity of this result.
One of the reasons this would be a huge result is that even a very expensive polynomial-time solution for any NP-complete problem (say, one which is O(n^2000) and would take several billion years to run against a 256-bit key) is only going to get faster over time. Also, the experience of cryptography is that once cracks start appearing in an algorithm the mathematicians start trying to wedge their chisels in and hammer those cracks into fractures, into holes, and eventually into whatever you call something which no longer resembles a crack so much it resembles absence-of-wall.
There are specific mechanisms by which this would happen, too. A near miss on P=NP would mean funding for professors looking into refining it, and professional interest generally, would suddenly explode. Nobody wants to fund or work on duds, but big contributions to this problem would make careers.
Not incidentally, while the government funds quite a bit of academic research, this particular branch of mathematics is of special interest to one type of government customer which has ways of getting funding for projects expedited if they are in the national interest... and it is virtually inconceivable that they would not find very, very strong national interest in the vicinity of this result.