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The P versus NP problem is a major unsolved problem in computer science. It asks whether every problem whose solution can be quickly verified can also be solved quickly. The general class of questions for which some algorithm can provide an answer in polynomial time is called "class P" or just "P".
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P != NP Proved by HP Labs researcher?
Being able to solve a problem as quickly as you can recognise a correct solution is a truly magical ability. It makes sense now. I love sudokus and I use the same strategy regardless of the difficulty level, which is I guess why harder sudokus take longer to solve? I would also love to know if someone discovers this magical strategy. Oh, you tricked me into reading about maths using money! Just kidding! Trying every solution is such a computer thing to do. I wonder how hard it would be to code other problem solving strategies.
Scientific Scribbles How Sudoku could win you a million dollars. Would you study math for this? Solving a Sudoku by trying all possibilities, starting from the top left. P versus NP this is the part where I explain how solving a Sudoku could win you one million dollars like I promised That brings us back to the Millennium Problems.
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Venn Diagrams! This is the P versus NP question.
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October 23, Categories Class of algorithms complexity Computer Science mathematics millennium problems p versus np sudoku. Posted by Matt Farrugia. Next Next post: Is my puppy smarter than me? Matt Farrugia says:. October 23, at pm. This asks whether the variables in a collection of logical statements can be chosen to make all the statements true, or whether the statements inevitably contradict each other. For each game, the team constructed sections of a level that force players to choose one of two paths — equivalent to assigning variables in the Boolean satisfiability problem. Arrangements of enemies and power-ups are equivalent to logical statements.
If they allow a level to be completed, that is equivalent to all the statements in the Boolean problem being true; if they make the level impossible, that is equivalent to a contradiction. Not every game in each series was included in the proof, as they follow different rules. For Mario, the team also prove that the games are NP-complete, an additional property with important consequences.
Many difficult problems can be converted into any problem in the NP-complete category. Then if you can solve the NP-complete problem — say, by completing a level of Mario — you have solved the original problem too. That includes the travelling salesman problem — finding the shortest route between a series of points — which is of real interest in the field of logistics, and also the knapsack problem, used in deciding how to allocate resources. So theoretically you could convert an example of either problem into a Mario level, and play the game to solve it.
Home Questions Tags Users Unanswered. Asked 7 years, 11 months ago. Active 1 month ago. Viewed 3k times. What will be the implications of this statement? Kaveh In mathematical logic, there are many sets of axioms people have considered. The independence of the Axiom of Choice from the Zermelo-Fraenkel set theory is a famous example. I voted to close as not a real question by mistake, but I meant to vote to close as off topic. As such, these conditional theorems would still have some value. Timothy Chow Timothy Chow 6, 30 30 silver badges 38 38 bronze badges.
But I'm not sure what your point is. The question is not whether a particular statement is undecidable , but whether it is neither true nor false. The two concepts are entirely distinct. Would you say, for example, that ZFC is neither consistent nor inconsistent? Everyone else that I know believes that either ZFC is consistent, or it isn't, even though we may have no way of determining which is the case.
Perhaps a less objectionable way of saying "X is neither true nor false" is that we have no a priori reason to prefer an axiomatic system in which X is true over an axiomatic system in which X is false. We have an almost universally agreed standard model of arithmetic; as a social convention, we accept arithmetic statements that hold in that model as being really, actually true.
The same cannot be said for set theory. Even if we grant you your personal religious beliefs, all you're saying is that you wouldn't join Aaronson and the rest of the world in declaring arithmetical sentences to be either true or false.
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We all agree that there's no way to tell from the form of a statement whether it's undecidable , but that's not the claim. The claim is that almost everyone except you does have strong intuitions that arithmetical statements are either true or false. Just because you don't share that conviction doesn't mean that others don't have it.
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Andrej Bauer Andrej Bauer My apologies. Kaveh Kaveh Avi Tal Avi Tal 1 1 gold badge 2 2 silver badges 8 8 bronze badges. Feel free to criticize. Thomas Eding Thomas Eding 1 1 silver badge 6 6 bronze badges. I imagine that if A exists, then one can simply analyze each enumerated program to see if it indeed solves an NP complete problem in polynomial time. I believe that since one is working with a finite instruction set given by some universal computer that A can be identified.
But I'm no expert.