# Tag Info

### Is there a task that is solvable in polynomial time but not verifiable in polynomial time?

This is only possible if there are many admissible outputs for a given input. I.e., when the relation $R$ is not a function because it violates uniqueness. For instance, consider this problem: ...
Accepted

### Assuming P = NP, how would one solve the graph coloring problem in polynomial time?

There are two cases: $P = NP$ non-constructively: this means we have derived a contradiction from the assumption that $P \neq NP$, and thus can conclude that $P = NP$ by the law of the excluded ...
Accepted

### How is the traveling salesman problem verifiable in polynomial time?

NP is the class of problems where you can verify "yes" instances. No guarantee is given that you can verify "no" instances. The class of problems where you can verify "no" instances in polynomial ...
Accepted

### Can a subset of an NP-complete problem be in P?

Your question doesn't make sense: The problem is NP-complete (proven) for all input data (without exception). This is not a thing. NP-completeness is a property of entire sets, not of specific ...
Accepted

### Evolving artificial neural networks for solving NP problems

No. This direction is unlikely to be useful, for two reasons: Most computer scientists believe that P $\ne$ NP. Assuming P $\ne$ NP, this means there does not exist any polynomial-time algorithm to ...
Accepted

### Is determining if there is a prime in an interval known to be in P or NP-complete?

So your problem is as follows: Input: integers $\ell,u$ Question: does there exist a prime in $[\ell,u]$? As far as I know, it is not known whether that problem is in P or not. Here's what I do know: ...
Accepted

### Is Post Correspondence Problem in NP?

The Post correspondence problem is undecidable, and in particular it is not in NP. The reason that your idea doesn't work is that the witness is not necessarily of polynomial size (in fact, you just ...

### False proofs that look correct

One of my favourites is the "brothers paradox": https://en.wikipedia.org/wiki/Boy_or_Girl_paradox I tell it as I learned it*, as follows: in a village, each family has two children, elder ...
Accepted

### Is detecting easy instances of NP-hard problems easy?

The problem isn't really well-posed. For any particular instance, there is a single solution, say $S$. Consequently, we can imagine an algorithm that has the answer $S$ hardcoded in: no matter what ...
Accepted

### Why rectangle packing is NP-hard but maybe not in NP?

In order for a language $L$ to be in NP, there needs to be a way to certify that instance $x$ belongs to $L$. This "way" is a polynomial size witness which can be verified in polynomial time....
Accepted

### is FIND WORDS in P?

Your language is in P. Suppose that the matrix is $n\times n$ and that the words have total length $\ell$. Each word can start at at most $n^2$ positions and be written in $O(1)$ many orientations, ...