# Questions tagged [separation]

Separation of complexity classes in computational complexity theory.

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### References for $\mathsf{PSPACE} \neq \mathsf{E}$ and $\mathsf{P} \neq \mathsf{NTIME}(n^k)$

In a recent blog post, Lance Fortnow dropped as a little exercise the task of proving $\mathsf{PSPACE} \neq \mathsf{E}$, using the fact that $\mathsf{EXP}$ is the closure of $\mathsf{E}$ under poly-...
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1 vote
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### Separating disjoint PSPACE-hard sets by NP-separators (and some variants)

I am trying to find some references or arguments for results of the form, where $X,Y$ vary over complexity classes, typically with $X\subseteq Y$, and $A,B$ are disjoint languages that are $Y$-hard: ...
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### How do separations of query complexities imply complexity class separations relative to oracles?

Simon's problem is the following: Given oracle access to a Boolean function $f: \{0,1\}^n\rightarrow \{0,1\}^n$, and promised that precisely one of the following two cases is true, decide which of ...
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### Can we efficiently distinguish between P and BPP?

Let's say algorithm $D$ distinguishes $BPP$ from $P$ if there exists a language $L \in BPP$ such that for all $A \in PTM$, $$D(\langle A\rangle) \in L \leftrightarrow D(\langle A \rangle) \notin L_A$$...
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### Could a descriptive complexity version of Rice's theorem be used to separate AC0 and PSPACE?

In this question, it was mentioned that there are descriptive complexity versions of Rice's theorem. I found a proof of the following theorem: Given a complexity class C, nontrivial properties of ...
1 vote
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### Separating the QIP hierarchy

Background: I'm a CS grad student. I've taken a course on computational complexity. Question: Can you suggest an introductory book on quantum computation, especially regarding the details of ...
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Show a function $f(n)$ which is space-constructible but not time-constuctible. Is this problem related to a possible separation between complexity classes DTIME(f(n)) and SPACE(f(n))?