\documentclass{article}\usepackage{charter}\usepackage{hyperref}\usepackage{amssymb}\usepackage{amsmath}\begin{document}\section*{Homework 2}\begin{enumerate}\item Give regular expressions for (a) decimal numbers and for (b) binary numbers. (Hint: Observe that the empty string is not a number. Also observe that leading 0s are normally not written.)\item Decide whether the following two regular expressions are equivalent $(\epsilon + a)^* \equiv^? a^*$ and $(a \cdot b)^* \cdot a \equiv^? a \cdot (b \cdot a)^*$.\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 $\texttt{""} \in L(r)$\end{center}\end{enumerate}\end{document}%%% Local Variables: %%% mode: latex%%% TeX-master: t%%% End: