Theory of Automata 1. (On Context-free Grammar) 1.1. Use pumping theorem to show that {a”b”a2nb2n.nz 1} is not context-free. 1.2. Is {a” b:n 0} context-free? If so, write a context-free no grammar, if not, prove it through pumping theorem a 1.3. Is {a2nb21:n 0} context-free? If so, write a context- free grammar; if not, prove it through pumping theorem. 1.4. If your answers for Q 1.2 and Q 1.3 are both yes, answer 1.4(a); If one of your answers is no, answer 1.4(b) 1.4(a) (1) Concatenation of context-free languages is context-free. (11) Concatenation of {a” b:n 20) and {a27b2n. na 0} gives {a”b”a2b2n. n 1) (II) So {a”b”a2b2n. n 1) is context-free What is wrong with the above argument? 1.4(b) Letc be some constant integer. Consider {acnbcn.n > 0). How many different c can make the language Show transcribed image text Theory of Automata 1. (On Context-free Grammar) 1.1. Use pumping theorem to show that {a”b”a2nb2n.nz 1} is not context-free. 1.2. Is {a” b:n 0} context-free? If so, write a context-free no grammar, if not, prove it through pumping theorem a 1.3. Is {a2nb21:n 0} context-free? If so, write a context- free grammar; if not, prove it through pumping theorem. 1.4. If your answers for Q 1.2 and Q 1.3 are both yes, answer 1.4(a); If one of your answers is no, answer 1.4(b) 1.4(a) (1) Concatenation of context-free languages is context-free. (11) Concatenation of {a” b:n 20) and {a27b2n. na 0} gives {a”b”a2b2n. n 1) (II) So {a”b”a2b2n. n 1) is context-free What is wrong with the above argument? 1.4(b) Letc be some constant integer. Consider {acnbcn.n > 0). How many different c can make the language

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Answer to Theory of Automata 1. (On Context-free Grammar) 1.1. Use pumping theorem to show that {a”b”a2nb2n.nz 1} is not context-f…