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Questions related to the (computational) complexity of solving problems

3 votes
1 answer
48 views

Prove that $\Sigma_{i}\text{SAT}$ is a complete problem for $\Sigma_{i}^{p}$

I'm trying to prove that $\Sigma_{i}\text{SAT}$ is a complete problem for $\Sigma_{i}^{p}$. Using induction on $i$, I can see that for the base case, when $i=1$, $\Sigma_{1}\text{SAT}$ is equivalent t …
itstwelvehere's user avatar
0 votes
1 answer
95 views

Negating a Quantified Boolean Formula (QBF)

I'm reading about quantified boolean formulas. One sentence mentions: You should also verify that the negation of the formula $Q_1x_1\cdot\cdot\cdot Q_nx_n \phi(x_1, ..., x_n)$ is the same as $Q^{\pr …
itstwelvehere's user avatar