Excercise 4. (Context-Free Languages) a) Give the formal definition of a context-free grammar. b) Let the context-free grammar G = ({S}, {0,1}, R, S) with rules / productions R be given as follows: S OSO 151016 Describe the language that is generated by G in your own words. c) Let the context-free language L = {w {G)}*(the parenthese pairs in w are properly nested} be given. Construct the pushdown automaton P (by giving its state transition dia- gram) that recognizes L, i.e. L(P) = L. d) Show that B= {a"b" ci<>