Question

1. Give a CFG for each of the following languages (with $n, m, k ge 0$). Note: You only need to give production rules for each grammar. (a) $L = {a^n b^{2n} mid n ge 2}$ (b) $L = {w in {a, b}^* mid n_a(w) = 3n_b(w)}$. (c) $L = {ww^R mid w in {a, b}^}$ (d) $L = {w in {a, b}^ mid w = w^R, ext{ that is, w is a palindrome.} }$ (e) $L = {a^n b^m mid n ge m + 3}$. (f) $L = {a^n b^m mid n < m + 3}$. (g) $L = {a^m b^n c^k mid m = n + k}$. (h) $L = {a^m b^n c^k mid n = k + m}$. (i) $L = {a^m b^n c^k mid n = m + 2k}$. (j) $L = {w in {a, b, c}^* mid n_a(w) + 2n_b(w) e n_c(w)}$. (k) $L = {a^m b^n c^k mid m > n ext{ or } n + m = k}$.

          1. Give a CFG for each of the following languages (with $n, m, k ge 0$).
Note: You only need to give production rules for each grammar.
(a) $L = {a^n b^{2n} mid n ge 2}$
(b) $L = {w in {a, b}^* mid n_a(w) = 3n_b(w)}$.
(c) $L = {ww^R mid w in {a, b}^*}$
(d) $L = {w in {a, b}^* mid w = w^R, 	ext{ that is, w is a palindrome.} }$
(e) $L = {a^n b^m mid n ge m + 3}$.
(f) $L = {a^n b^m mid n < m + 3}$.
(g) $L = {a^m b^n c^k mid m = n + k}$.
(h) $L = {a^m b^n c^k mid n = k + m}$.
(i) $L = {a^m b^n c^k mid n = m + 2k}$.
(j) $L = {w in {a, b, c}^* mid n_a(w) + 2n_b(w) 
e n_c(w)}$.
(k) $L = {a^m b^n c^k mid m > n 	ext{ or } n + m = k}$.

1. Give a CFG for each of the following languages (with n, m, k ge 0).
Note: You only need to give production rules for each grammar.
(a) L = a^n b^2n mid n ge 2
(b) L = w in a, b^* mid na(w) = 3nb(w).
(c) L = ww^R mid w in a, b^*
(d) L = w in a, b^* mid w = w^R, ext that is, w is a palindrome.
(e) L = a^n b^m mid n ge m + 3.
(f) L = a^n b^m mid n < m + 3.
(g) L = a^m b^n c^k mid m = n + k.
(h) L = a^m b^n c^k mid n = k + m.
(i) L = a^m b^n c^k mid n = m + 2k.
(j) L = w in a, b, c^* mid na(w) + 2nb(w)
e nc(w).
(k) L = a^m b^n c^k mid m > n ext or n + m = k.

Added by Claudia E.

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