1. Draw a minimal DFA that accepts the following character set, if possible. If no DFA can be created, explain why it isn't possible. Use the following alphabet: ={a, b, c, d}.

"The set of all strings (including the empty string) such that all 'c' characters appear before any 'a' character and that contain no two consecutive instances of the character 'b'." 2. Consider the grammar below and the token string: num+num*(num+num) a. Show a leftmost derivation of the string. b. Show a rightmost derivation of the string. c. Show the parse tree (not AST) corresponding to the leftmost derivation you gave in part (a). d. Would the parse tree corresponding to a rightmost derivation be the same as you came up with in part (c)? Why or Why not? Grammar: expr -> expr addop term | term addop -> + | - term -> term mulop factor | factor mulop -> * factor -> (expr) | num