Create a free Team What is Teams? Collectives on Stack Overflow. Learn more. Asked 13 years, 3 months ago. Active 1 year, 8 months ago. Viewed k times. There would be no special value in "creative leaps," no fundamental gap between solving a problem and recognizing the solution once it's found.
Everyone who could appreciate a symphony would be Mozart; everyone who could follow a step-by-step argument would be Gauss Add a comment. Active Oldest Votes. P stands for polynomial time. NP stands for non-deterministic polynomial time. Andrew Campbell 3 1 1 silver badge 2 2 bronze badges. Dima Dima It isn't true that the only way to solve SAT is enumeration of cases. See en.
Derek, I beg to disagree. I really don't see how you explain P and NP without Turing machines. I was once in an algorithms class, which tried that. If I didn't know about TM's, I'd be totally lost. Conversely if it was proved that P! I know this is quite old, but I just wanna say that the answer is epic and it's the first that clicked for me! Good job — Dimitar Dimitrov. Correction in the second to last paragraph: "we would be certain that there is no way to solve an NP Complete problem in polynomial time on a conventional computer", since P is a subset of NP and proving P!
Show 15 more comments. A yes-or-no problem is in P P olynomial time if the answer can be computed in polynomial time. A yes-or-no problem is in NP N on-deterministic P olynomial time if a yes answer can be verified in polynomial time. Carlos F 4 4 silver badges 10 10 bronze badges. Derek Park Derek Park To give the simplest answer I can think of: Suppose we have a problem that takes a certain number of inputs, and has various potential solutions, which may or may not solve the problem for given inputs.
David Thornley David Thornley In your second last paragraph you have "in a way, the hardest sort". You should say NP-complete are the hardest since they are NP-hard.
I'm not sure that fortune would be yours. The government might want your head. And it's a pretty inspiring problem. Ajit Panigrahi 11 11 silver badges 24 24 bronze badges.
That's not quite true - you can convert a NDTM to a DTM, but the new machine has a running time exponential in the running time of the original you effectively breadth first search the state transition graph of the NDTM. Lucky Put simply, A problem L is NP-complete if 1 L is in P, and 2 an algorithm which solves L can be used to solve any problem L' in NP; that is, given an instance of L' you can create an instance of L that has a solution if and only if the instance of L' has a solution.
Formally speaking, every problem L' in NP is reducible to L. Hence, if 3-coloring of graphs is NP-complete, so is boolean-formula-satisfiability. The Overflow Blog. Solving some problems can take an algorithm an amount of time proportional to 2 N , 3 N , and so on. In this case, N is the exponent, meaning that every element the algorithm has to deal with increases its complexity exponentially. In this case, the algorithm can be completed in exponential time, or NP which really stands for nondeterministic polynomial time.
The difference between these two can be huge. If a P algorithm has elements, and its time to complete working is proportional to N 3 , then it will solve its problem in about 3 hours. Are these two flavor of problems irrevocably separate from one another? Are some problems simply complex by their fundamental nature? If P does equal NP , then it would have some major implications for our way of life. One major benefit is that many NP problems are referred to as being NP -complete, which means that their solutions can be quickly adapted to any other NP -complete problem.
So, developing a way to quickly solve one NP -complete problem would make significant strides towards completing all other NP -complete problems. What are some examples of NP problems? Many researchers focus on one major concern. The majority of modern cryptography relies on codes that are hard to crack but easy to check.
As an example, consider the passwords or PINs to your various accounts. Checking that they are correct is straightforward, but brute-force guessing every permutation of letters and numbers would take forever. The encryption behind securing your credit card number when ordering something on Amazon, too, is an example of NP cryptography. And in real life, NP-complete problems are fairly common, especially in large scheduling tasks. The most famous NP-complete problem, for instance, is the so-called traveling-salesman problem: given N cities and the distances between them, can you find a route that hits all of them but is shorter than … whatever limit you choose to set?
Peter's breakthrough inspired an enormous amount of research both in the computer science community and in the physics community. But that now seems unlikely: the factoring problem is actually one of the few hard NP problems that is not known to be NP-complete. I think it has helped bridge the mathematics and computer science communities. Massachusetts Institute of Technology. Search MIT. Search websites, locations, and people. Enter keywords to search for news articles: Submit.
Browse By. Explained: P vs. The most notorious problem in theoretical computer science remains open, but the attempts to solve it have led to profound insights. Publication Date :.
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