Consider the following context-free grammars: 1. S0S101 with string 00011. 2. S>+SSSS a with string + aaa. 3. S>S+SSS(S)S a with string (a+a)a For each grammar: a) Give a leftmost derivation for the string. b) Give a rightmost derivation for the string. c) Give a parse tree for the string. d) Is the grammar ambiguous or unambiguous? Justify your answer. e) Describe the language generated by this grammar. Problem 1: Considering the alphabet {a,b} derive a Non-Deterministic-Finite Automaton (NFA) using the Thompson construction that is able to recognize the sentences generated by the regular expression b(abbba)b. Does the sentence w= "abbb" belong to the language generated by this regular expression? Justify