5. (a) What is the language of the following NFA? Give all the computations of the automaton on the input word $a b$. (3 marks) (b) What is the language over $\{a, b\}$ defined by the following context-free grammar with start variable $S$ : (3 marks) $$ \begin{array}{1} S ightarrow X, \quad S ightarrow Y X ightarrow a Xb, \quad X ightarrow X b, \quad X ightarrow b, W Y ightarrow a Yb, \quad Y ightarrow a Y, \quad Y ightarrow a . \end{array} $$ (c) Define the language $L=\left\{a^{k} b^{1} a^{n} b^{m} \mid k+1=m+n ight\}$ by means of a context-free grammar. Show the derivation of the word $a bbba a b b$ in your CFG. (4 marks) CS.VS.981