1. Write regular expressions to recognize comments in C. Single line comments begin with // and end with the first newline character. Comments that may span multiple lines are delimited by /* and */. You may use a not operator.
2. Build a nested-case-statements finite automaton that converts all letters in its input to lower case, except within C-style comments.
3. Consider the following grammar:

G S $$

S A M

M S |

A a E | b A A

E a B | b A |

B b E | a B B

1. Which of the following strings are in the language generated by this grammar: b a a b a $$, a b b a $$, b b a a $$? For each string in the language, show a possible derivation.
2. Show that the grammar is ambiguous by finding an example of a string with two valid parse trees.
3. Show the steps in constructing a parse tree for the input string a b a $$ using a bottom-up approach (shift-reduce parser).