diff options
| -rw-r--r-- | ps1/main.tex | 2 | ||||
| -rw-r--r-- | ps2/main.tex | 6 |
2 files changed, 4 insertions, 4 deletions
diff --git a/ps1/main.tex b/ps1/main.tex index b773275..8473bf5 100644 --- a/ps1/main.tex +++ b/ps1/main.tex @@ -32,7 +32,7 @@ \newtheorem{lemma}{Lemma} \author{Thibaut Horel} -\title{CS 229r Problem Set 1 -- Solutions} +\title{CS 224 Problem Set 1 -- Solutions} \begin{document} diff --git a/ps2/main.tex b/ps2/main.tex index c4a4ad3..360d88a 100644 --- a/ps2/main.tex +++ b/ps2/main.tex @@ -34,7 +34,7 @@ \newtheorem{lemma}{Lemma} \author{Thibaut Horel} -\title{CS 229r Problem Set 2 -- Solutions} +\title{CS 224 Problem Set 2 -- Solutions} \begin{document} @@ -235,7 +235,7 @@ determined once $h(x)$, $h(y)$ and $h(z)$ have been observed. \item By construction all the elements in $T'$ have different characters at position 0 and different from the characters at position 0 of the words in $T'$. Hence, the given words - in $T$, $\mathca{H}$ behaves completely randomly on $T'$ by the + in $T$, $\mathcal{H}$ behaves completely randomly on $T'$ by the same observation as the one we used in \textbf{(b)}. But by the induction hypothesis, $\mathcal{H}$ behaves completely randomly on $T$. As a consequence $\mathcal{H}$ behaves completely randomly on @@ -257,7 +257,7 @@ where the second inequality follows from the lemma. Now applying a union bound: \Pr[l\geq k] &\leq \sum_{S,\, |S| = \log k}\Pr[S\text{ maps to $L$ and $\mathcal{H}$ random over $S$}]\\ &\leq\binom{n}{\log k}m\frac{1}{m^{\log k}} - \leq\frac{n^\log k}{(\log k)!}\frac{1}{m^{\log k -1}} + \leq\frac{n^{\log k}}{(\log k)!}\frac{1}{m^{\log k -1}} \end{align*} Using $m> n^{1.01}$, we get: \begin{displaymath} |