: [ E \to E + T \mid T ] [ T \to T \times F \mid F ] [ F \to (E) \mid a \mid b ]
Better approach — known correct grammar: [ S \to aSb \mid aSbb \mid \varepsilon ] For m=3, n=2: S → aSbb → a(aSb)bb → aa(ε)bbbb? No — that’s 4 b’s. So maybe n=2, m=3 not possible? Actually it is: ( a^2 b^3 ) = a a b b b. Let’s test:
So the sequence of rules: aSbb then aSb then ε. Good. So grammar works. Language : ( w \in a,b^* \mid w = w^R )
: [ S \to aS \mid bS \mid \varepsilon ] Wait — that gives any length. Let's fix:
: [ S \Rightarrow aSb \Rightarrow aaSbb \Rightarrow aaaSbbb \Rightarrow aaabbb ] 5. Example 4 – ( a^n b^m ) with ( n \le m \le 2n ) Language : ( a^n b^m \mid n \ge 0, m \ge n, m \le 2n )
: [ E \to E + T \mid T ] [ T \to T \times F \mid F ] [ F \to (E) \mid a \mid b ]
Better approach — known correct grammar: [ S \to aSb \mid aSbb \mid \varepsilon ] For m=3, n=2: S → aSbb → a(aSb)bb → aa(ε)bbbb? No — that’s 4 b’s. So maybe n=2, m=3 not possible? Actually it is: ( a^2 b^3 ) = a a b b b. Let’s test: cfg solved examples
So the sequence of rules: aSbb then aSb then ε. Good. So grammar works. Language : ( w \in a,b^* \mid w = w^R ) : [ E \to E + T \mid
: [ S \to aS \mid bS \mid \varepsilon ] Wait — that gives any length. Let's fix: Actually it is: ( a^2 b^3 ) = a a b b b
: [ S \Rightarrow aSb \Rightarrow aaSbb \Rightarrow aaaSbbb \Rightarrow aaabbb ] 5. Example 4 – ( a^n b^m ) with ( n \le m \le 2n ) Language : ( a^n b^m \mid n \ge 0, m \ge n, m \le 2n )