diff -r e85600529ca5 -r 4794759139ea hw02.tex --- a/hw02.tex Sat Jun 15 09:11:11 2013 -0400 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,36 +0,0 @@ -\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: