Cfg Solved Examples -

S → aSbb → a(aSbb)bb → aa(ε)bbbb → aabbbb (wrong). So that’s 4 b’s, not 3.

: [ S \to aSbS \mid bSaS \mid \varepsilon ]

Derivation for abba : [ S \Rightarrow aSbS \Rightarrow a\varepsilon bS \Rightarrow abS \Rightarrow abbSaS \Rightarrow abb\varepsilon a\varepsilon = abba ] Language : Valid arithmetic expressions with a, b, +, *, (, ) cfg solved examples

: [ S \Rightarrow aSa \Rightarrow aba ] 7. Example 6 – ( a^i b^j c^k ) with i+j = k Language : ( a^i b^j c^i+j \mid i,j \ge 0 )

: [ S \to aS \mid bS \mid \varepsilon ] Wait — that gives any length. Let's fix: S → aSbb → a(aSbb)bb → aa(ε)bbbb → aabbbb (wrong)

: [ S \to aSa \mid bSb \mid a \mid b \mid \varepsilon ]

: [ E \to E + T \mid T ] [ T \to T \times F \mid F ] [ F \to (E) \mid a \mid b ] Example 6 – ( a^i b^j c^k )

: [ S \Rightarrow SS \Rightarrow (S)S \Rightarrow ((S))S \Rightarrow (())S \Rightarrow (())(S) \Rightarrow (())() ] 4. Example 3 – ( a^n b^n ) (equal number of a’s and b’s) Language : ( a^n b^n \mid n \ge 0 )