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4
votes
1answer
56 views

Is $BQP$ in $P^{NP}$?

I read in the introduction of this paper http://www.scottaaronson.com/papers/uncompute.pdf that there is a problem $B$ such that $BQP^B \not\subset P^{NP^B}$, and that $B$ is in $BPP$. But, using ...
3
votes
0answers
90 views

Relativization of NP-completeness

This is actually exercise 3.7 from "Computational Complexity: A Modern Approach". I need to prove that the NP-Completeness of 3-sat does not relativize, i.e. I need to show that that exists some ...
4
votes
2answers
92 views

The meaning of relativization

I don't understand the notion of relativization. I expose with an example. Consider a class $A$ that contains $P$, e.g. $NP$. Why $P^A$ is not necessarily equal to $A$? I can naively think that if one ...
3
votes
1answer
154 views

Is it axiomatic that the Time Hierarchy Theorem holds true in all relativized worlds?

I learned from this post that ${\sf DTIME}^{\text{EXP}}(n^k) \neq \text{EXP}$ for a fixed $k$ for otherwise the Time Hierarchy Theorem would fail in that relativized world. However, is it possible to ...
1
vote
1answer
31 views

Why does the principle of locality of computation not relativize?

Although I have trouble understanding oracle TMs, I appreciate that non-relativizing techniques will be needed to resolve P vs. NP (as well as most other open problems in TCS). However, one of the ...
4
votes
1answer
151 views

Why are non-relativizing proofs preferred to relativizing ones?

I apologize, but even after these two other posts: here and here I'm still having trouble understanding oracle TMs and relativization. This question comes at the issue from a different angle: Why ...
2
votes
1answer
196 views

Why does the Time Hierarchy Theorem not relativize?

Is it true that $DTIME^A(n^k) = EXP$ for any fixed $k$ and EXPTIME-complete oracle $A$? If not, what do these complexity classes equal and why (because I know that $P^A = EXP$ for any ...
7
votes
1answer
346 views

Intuition behind Relativization

I take course on Computational Complexity. My problem is I don't understand Relativization method. I tried to find a bit of intuition in many textbooks, unfortunately, so far with no success. I will ...
9
votes
2answers
833 views

An oracle to separate NP from coNP

How to prove that $\mathsf{NP}^A \neq \mathsf{coNP}^A$ ? I am just looking for a such oracle TM $M$ and a recursive language $L(M) = L$ for which this holds. I know the proof where you show that ...
18
votes
3answers
849 views

Why is Relativization a barrier?

When I was explaining the Baker-Gill-Solovay proof that there exists an oracle with which we can have, $\mathsf{P} = \mathsf{NP}$, and an oracle with which we can have $\mathsf{P} \neq \mathsf{NP}$ to ...