diff -r 13ff10d9717a -r 04264d0c43bb hws/hw02.tex --- a/hws/hw02.tex Mon Oct 07 09:34:12 2013 +0100 +++ b/hws/hw02.tex Mon Oct 07 09:45:11 2013 +0100 @@ -14,7 +14,9 @@ in general for arbitrary languages $A$, $B$ and $C$: \begin{eqnarray} (A \cup B) @ C & = & A @ C \cup B @ C\nonumber\\ -A^* \cup B^* & = & (A \cup B)^*\nonumber\\ A^* @ A^* & = & A^*\nonumber\\ (A \cap B)@ C & = & (A@C) \cap (B@C)\nonumber +A^* \cup B^* & = & (A \cup B)^*\nonumber\\ +A^* @ A^* & = & A^*\nonumber\\ +(A \cap B)@ C & = & (A@C) \cap (B@C)\nonumber \end{eqnarray} \noindent @@ -36,8 +38,6 @@ \item Given the regular expression $r = (a \cdot b + b)^*$. Compute what the derivative of $r$ is with respect to $a$ and $b$. Is $r$ nullable? -\item What is a regular language? - \item Prove that for all regular expressions $r$ we have \begin{center} $\text{nullable}(r)$ \quad if and only if \quad $\texttt{""} \in L(r)$