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Computational complexity classes and their relations

14 votes
0 answers
233 views

Do circuits allow to derive EXPSPACE hardness results?

It seems that encoding an NP-complete problem succinctly often makes it nexptime-complete. For instance, 3SAT or HAMILTONIAN PATH become NEXPTIME-complete when the encoding is succint, eg using circui …
Abdallah's user avatar
  • 813
1 vote
0 answers
66 views

Is anything known about NC$^1$ with NP oracle

A few things are known about the class $\textsf{L}$ provided with an $\textsf{NP}$ oracle ($\textsf{L}^\textsf{NP} = \Theta_2^\textsf{P}$ has attracted a bit of attention, for instance [1]) On the oth …
Abdallah's user avatar
  • 813
2 votes
0 answers
84 views

Logarithmic queries to $\Sigma_i^P$ oracle and the Boolean hiearchies

If I understood correctly (the complexity zoo, wikipedia, and some of the cited articles), the class $\textsf{P}^{\textsf{NP}[\log]}$, also known as $\Theta_2^{\textsf{P}}$, sits at the top of the Boo …
Abdallah's user avatar
  • 813