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The terminology in the text misses the mark a bit. - P and NP are not disjoint sets. NP just means "verifiable in polynomial time." There are plenty of easy
by peeters 13y ago
The terminology in the text misses the mark a bit.
- P and NP are not disjoint sets. NP just means "verifiable in polynomial time." There are plenty of easy problems to solve that are verifiable in polynomial time. P is in fact a subset of NP.
- NP-hard problems are ones that are difficult for computers to solve
- NP-complete is the intersection between NP-hard and NP
Furthermore, it presents the P vs NP problem as an attempt by mathematicians to solve P = NP, whereas almost no mathematicians believe P = NP, they're just all trying to prove that P != NP.
- danielrm26 13y agoApologies. I was trying to keep it as simple as possible. I don't think people who need to know it to that degree will even need the summary I provided.
- peeters 13y agoI think keeping it simple is great, but you should bring your terminology in the text to be consistent with the diagram at the start, otherwise it's confusing. I don't think it would be difficult to say something like: > P and NP are two different kinds of problems. P problems are easy for computers to solve, and NP problems are easy for computers to check answers for. All P problems are NP problems; that is, if it's easy for the computer to solve, it's easy to verify the solution. The P vs NP problem asks: within the class of NP problems, are there problems which are not P, that is, which are not easy for computers to solve?
- danielrm26 13y agoCan I use that?
- peeters 13y agoBy all means.
- danielrm26 13y agoUpdated. Thanks for the input.
- parfitt 13y agoThank you. That is a wonderful description of what the P vs NP problem is all about.