Let G be the G: S -> aSb | SS | ab a) Give a left-most derivation of w= aaabbb following context-free grammar. b) Give a leftmost derivation of w= aaabbabb

24. Show that the grammars and are not equivalent. S → aSb|bSa|SS|a S aSb|bSala

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'

5. Construct npda that accept the following context-free grammars: (a)     S -> aAB | bBB     A -> aA | bB | b     B -> b   (b)     S -> ABb | a | b     A -> aaA | Ba     B -> bb

Construct a Chomsky normal form grammar for L(G) for the following cfg G: G=({S,B}, {a,b,c,d}, {S→Sb|Ba, B→BdBc|S|ɛ}, S). Note: You must first remove all & and all unit productions.