36 $(a \cdot b)^* \cdot a \equiv^? a \cdot (b \cdot a)^*$.

    36 $(a \cdot b)^* \cdot a \equiv^? a \cdot (b \cdot a)^*$.

    37 

    37 

    38 \item Given the regular expression $r = (a \cdot b + b)^*$. Compute what the derivative of $r$ is with respect to

    38 \item Given the regular expression $r = (a \cdot b + b)^*$. Compute what the derivative of $r$ is with respect to

    39 $a$ and $b$. Is $r$ nullable?

    39 $a$ and $b$. Is $r$ nullable?

    40 

    40 

    43 \item Prove that for all regular expressions $r$ we have

    41 \item Prove that for all regular expressions $r$ we have

    44 \begin{center}

    42 \begin{center}

    45 $\text{nullable}(r)$ \quad if and only if \quad $\texttt{""} \in L(r)$

    43 $\text{nullable}(r)$ \quad if and only if \quad $\texttt{""} \in L(r)$

    46 \end{center}

    44 \end{center}

    47 

    45