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Explain the proof by Vinay Deolalikar that P != NP [closed]

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问题 Closed. This question is off-topic. It is not currently accepting answers. Want to improve this question? Update the question so it's on-topic for Stack Overflow. Closed 2 years ago . Recently there has been a paper floating around by Vinay Deolalikar at HP Labs which claims to have proved that P != NP. Could someone explain how this proof works for us less mathematically inclined people? 回答1: I've only scanned through the paper, but here's a rough summary of how it all hangs together. From

“Finding all the code in a given binary is equivalent to the Halting problem.” Really?

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问题 Was just reading the highly voted question regarding Emulators and the statement It's been proven that finding all the code in a given binary is equivalent to the Halting problem. Really stuck out at me. Surely that can't be true? Isn't it just a large dependency graph? Would be really grateful for some further insight into this statement. 回答1: I believe what is meant is "finding all code that is ever executed", i.e. finding coverage, possibly in combination with dynamically generated code.

Reduction of A to B : True or False

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问题 There are two statements: If a decision problem A is polynomial-time reducible to a decision problem B (i.e., A≤ pB ), and B is NP-complete, then A must be NP-complete. And: If a decision problem B is polynomial-time reducible to a decision problem A (i.e., B≤ pA ), and B is NP-complete, then A must be NP-complete. Which of the above statements are true? Can you also give explanation? 回答1: the first statement is false because it means that by solving B and then applying some polynomial time

3SAT solved in polynomial time?

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问题 I have seen few errors in the cnf files for both satisfiable and unsatisfiable clauses files SATLIB Benchmark Problems To be more specific I have found out that the 1st file of the zip folder here: 20 variables, 91 clauses - 1000 instances, all satisfiable contains a file with the title of "uf20-01", the equation of which is unsatisfiable clearly as the 7th clause at the 15th line and the 87th clause at line number 4 are both exact inverse of each other!((5 19 17) and (-5 -19 -17)) Thus an

What are NP problems?

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问题 I read the article on wikipedia but could not understand what exactly are NP problems. Can anyone tell me about them and also what is relation of them with P Problems? 回答1: NP problems are problems that given a proposed solution, you can verify the solution in a polynomial time. For example, if you have a list of University courses and need to create a schedule so that courses won't conflict, it would be a really difficult task (complexity-wise). However, given a proposed schedule, you can

NP-hard problems that are not NP-complete are harder?

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问题 From my understanding, all NP-complete problems are NP-hard but some NP-hard problems are known not to be NP-complete, and NP-hard problems are at least as hard as NP-complete problems. Is that mean NP-hard problems that are not NP-complete are harder? And how it is harder? 回答1: To answer this question, you first need to understand which NP-hard problems are also NP-complete. If an NP-hard problem belongs to set NP, then it is NP-complete. To belong to set NP, a problem needs to be (i) a

Explain the proof by Vinay Deolalikar that P != NP [closed]

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Recently there has been a paper floating around by Vinay Deolalikar at HP Labs which claims to have proved that P != NP . Could someone explain how this proof works for us less mathematically inclined people? Michael Anderson I've only scanned through the paper, but here's a rough summary of how it all hangs together. From page 86 of the paper. ... polynomial time algorithms succeed by successively “breaking up” the problem into smaller subproblems that are joined to each other through conditional independence. Consequently, polynomial time algorithms cannot solve problems in regimes where

Why are NP problems called that way (and NP-hard and NP-complete)?

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Really.. I'm having the last test for graduation this Tuesday, and that's one of the things I just never could understand. I realize that a solution for NP problem can be verfied in polynomial time. But what does determinism has to do with that? And if you could explain me where NP-complete and NP-hard got their names, that would be great (I'm pretty sure I get the meaning of them, I just don't see what their names have to do with what they are). Sorry if that's trivial, I just can't seem to get it (-: Thanks all! P Class of all problems which can be solved by a deterministic Turing machine in

What's “P=NP?”, and why is it such a famous question? [closed]

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The question of whether P=NP is perhaps the most famous in all of Computer Science. What does it mean? And why is it so interesting? Oh, and for extra credit, please post a proof of the statement's truth or falsehood. :) P stands for polynomial time. NP stands for non-deterministic polynomial time. Definitions: Polynomial time means that the complexity of the algorithm is O(n^k), where n is the size of your data (e. g. number of elements in a list to be sorted), and k is a constant. Complexity is time measured in the number of operations it would take, as a function of the number of data items

Why are NP problems called that way (and NP-hard and NP-complete)?

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问题 Really.. I'm having the last test for graduation this Tuesday, and that's one of the things I just never could understand. I realize that a solution for NP problem can be verfied in polynomial time. But what does determinism has to do with that? And if you could explain me where NP-complete and NP-hard got their names, that would be great (I'm pretty sure I get the meaning of them, I just don't see what their names have to do with what they are). Sorry if that's trivial, I just can't seem to