3. For a string we {a, b, c}*, let us denote by na(w) the number of...

    

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3. For a string we {a, b, c}*, let us denote by na(w) the number of a's in w, by n,(w) the number of b's in w, and by n,(w) the number of c's in w. (a) Design a general (unrestricted) grammar for the language Labc {we {a,b,c}* | na(w) = n(w)= n(w)}. Give a derivation in your grammar for the string cabacb Labc (b) Prove (precisely!) that the language Labe is not context-free. 15 points 3. For a string we {a, b, c}*, let us denote by na(w) the number of a's in w, by n,(w) the number of b's in w, and by n,(w) the number of c's in w. (a) Design a general (unrestricted) grammar for the language Labc {we {a,b,c}* | na(w) = n(w)= n(w)}. Give a derivation in your grammar for the string cabacb Labc (b) Prove (precisely!) that the language Labe is not context-free. 15 points