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COMPUTER SCIENCE
Consider the function pad : $\Sigma^{*} \times \mathcal{N} \longrightarrow \Sigma^{*} \#^{*}$ that is defined as follows. Let pad(s, l)=$s \# ^{j}$, where j=max(0, l−m) andm is the length of s.
Thus, pad(s, l) simply adds enough copies of the new symbol # to the end of s so that the length of the result is at least l. For any language A and function $f: \mathcal{N} \longrightarrow \mathcal{N}$, the language pad(A, f) as pad(A, f)={pad(s, f(m))| where $s \in A$ and m is the length of s}. Prove that if $A \in \operatorname{TIME}\left(n^{6}\right)$, then $\operatorname{pad}\left(A, n^{2}\right) \in \operatorname{TIME}\left(n^{3}\right)$.
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COMPUTER SCIENCE
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