Question
Show that for any problem $\Pi$ in $\mathbf{N P}$, there is an algorithm which solves $\Pi$ in time $O\left(2^{p(n)}\right),$ where $n$ is the size of the input instance and $p(n)$ is a polynomial (which may depend on $\Pi$ ).
Step 1
Since the problem $\Pi$ is in $\mathbf{N P}$, there exists a non-deterministic Turing machine (NTM) $M$ that can solve $\Pi$ in polynomial time, say $p(n)$, where $n$ is the size of the input instance. Show more…
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