Star One Tv Serial Remix All Epi
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How to prove that a $QP$ equivalence problem can be in $\mathbf{P}$?
The question is as follows.
How to prove that an instance of an $QP$ equivalence problem can be
in $\mathbf{P}$?
Unfortunately, I have nothing concrete to start a proof.
A:
We can suppose that $Q$ is a non deterministic polynomial time (i.e. $Q$ does not necessarily accept in time polynomial in $|I|$) language and that $P$ is a deterministic language.
Consider an algorithm $\mathcal{A}$ deciding $P$:
$\mathcal{A}$ runs in polynomial time.
The length of the program executed by $\mathcal{A}$ is bounded by a polynomial in $|I|$.
The output of $\mathcal{A}$ is a YES or NO answer.
Now, for all $i\in\{0,1\}^*$, $\mathcal{A}$ has access to a deterministic machine $M_i$ that takes as input a program $\pi_i$ of length less than the bound and decides in deterministic time polynomial in $|\pi_i|$
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