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Questions related to the (computational) complexity of solving problems

5 votes

How to prove that problem is not in P

The generally easiest solution for this kind of thing is to assume that you can do it, and show that it contradicts a well-established result. The easiest case will be when you can show that the pro …
Patrick Collins's user avatar
7 votes
2 answers
2k views

Generating a set of minimal-length strings that, together, invoke every production of a cont...

Problem (tl;dr) Given a context free grammar, $G$, find a set of strings that take $G$ through every production it has at least once. How and how fast can it be done? Background I'm working on a …
Patrick Collins's user avatar
0 votes

Is P^SAT with only one query equal to the union of NP and coNP?

Hint (noting the homework tag on the other post): $P^{SAT}$, by the Cook-Levin theorem, is the same as an $NP$ oracle. Given that $\text{co-}NP \neq NP$, what does this imply?
Patrick Collins's user avatar