CS 332 HW 2 - Grammars, Languages, FSM, and PDA Do your work on a separate page. Turn in this page as a cover sheet. Do not staple, fold, clip, 1, (30 pts) Given alphabet -(a, b }, define Li-(a + b)"(aa)"bb. or otherwise attach your papers together. Write your name on each sheet. (a) Write a regular grammar, Ci, for L1 (b) Draw a deterministic Finite State Machine for L1. (c) Draw the parse tree for the string u baaabb. (d) is your grammar ambiguous? 2" (30 pts) Given alphabet = {a, b }, define L2-any string of length two or more having the same number of a's as b's, though they may appear in any order. (a) Write a Context Free Grammar, G2, for L2. (b) Draw a Push Down Automata for L1. (c) Draw the parse tree for the string u baaabb. (d) Is your grammar ambiguous