\documentclass{article}\usepackage{charter}\usepackage{hyperref}\usepackage{amssymb}\usepackage{amsmath}\begin{document}\section*{Homework 3}\begin{enumerate}\item What is a regular language?\item Assume you have an alphabet consisting of the letters $a$, $b$ and $c$ only.(1) Find a regular expression that recognises the two strings $ab$ and $ac$. (2)Find a regular expression that matches all strings \emph{except} these two strings.Note, you can only use regular expressions of the form \begin{center}$r ::= \varnothing \;|\; \epsilon \;|\; c \;|\; r_1 + r_2 \;|\; r_1 \cdot r_2 \;|\; r^*$\end{center}\item Define the function $zeroable$ which takes a regular expression as argumentand returns a boolean. The function should satisfy the following property:\begin{center}$zeroable(r)$ \;if and only if\; $L(r) = \varnothing$\end{center}\item Define the tokens and regular expressions for a languageconsisting of numbers, left-parenthesis (, right-parenthesis ),identifiers and the operations $+$, $-$ and $*$. Can the following strings in this language be lexed?\begin{itemize}\item \texttt{"}$(a + 3) * b$\texttt{"}\item \texttt{"}$)()++ -33$\texttt{"}\item \texttt{"}$(a / 3) * 3$\texttt{"}\end{itemize}In case they can, can you give the corresponding token sequences.\end{enumerate}\end{document}%%% Local Variables: %%% mode: latex%%% TeX-master: t%%% End: