2. Construct a context-free grammar G to accept the set of strings over the alphabet {(,)} that are not balanced. Explain the role of the each nonterminal and state the language generated by each of them. Exhibit leftmost derivations for the strings w1 = ())(, w2 = ((()) and w3 = ) in your grammar G.

Is the grammar LL(1)? Why or why not? If grammar is LL(1), use your parsing table to derive the string: modifier noun verb modifier

Question 3 a) Consider the grammar E → E + E | E ∗ E | (E) | id. I. Change ambiguous grammar to non-ambiguous? II. Give a context-free grammar for generating the set of palindromes over the alphabet a,b. III. Give a context-free grammar for generating all strings over a,b such that | a |= 2∗ | b

Question 2-Context-free Grammars Consider the alphabet = {A, V., (,), x, y, z) and the following grammar G = (V,E, R, F), defined by the rules: F (FAF) | (FVF) | (F) | P (a) Identify the set of variables and the set of terminal symbols of G. (b) Identify three words (of lengths between 10 and 20) that can be generated by the above grammar and show their derivations. (c) Consider a modified grammar G', where we remove the brackets '(' and ')' from the alphabet and the derivation rules. That is we set Σ'= {A, V., x, y, z) and we remove all occurrences of brackets in the derivation rules. Show that there are words that are derived ambiguously in G'

The set of all syntactically valid strings representing regular expressions is A. a regular language, because a regular expression can describe this language B. a context-free language and it can be generated by a context-free grammar but not by any regular grammar O C. a context-sensitive language but not by any context-free grammar