Context Sensitive Grammars

Question

Is the following CSG for a^n b^n c^n correct?

S->aSbC|abc

Cb->bC

C->c

If not please explain why?

Comments

What is n?

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It is generating aabcbc , So wrong

Answer 1

Below is the grammar for L = {a^n b^n c^n | n>=1}

S → abc | aSAc

cA → Ac

bA → bb 

Let’s try deriving string w = aaabbbccc

S → aSAc                 [S → aSAc]

   → aaSAcAc           [S → aSAc]

   → aaSAAcc           [cA → Ac]

   → aaabcAAcc       [S → abc]

   → aaabAcAcc       [cA → Ac]

   → aaabAAccc       [cA → Ac]

   → aaabbAccc       [bA → bb]

   → aaabbbccc       [bA → bb] 

Comments

Because of cA --> Ac is not in CSG isn't it? Can u write CSG grammar for this