Question

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Context-sensitive grammar and Context-free grammar

In my textbook, here is the explain of these two terms :

Context Sensitive Grammar:

grammar can have productions of the form w1 → w2, where w1 = lAr and
w2 = lwr, where A is a nonterminal symbol, l and r are strings of zero
or more terminal or nonterminal symbols, and w is a nonempty string of
terminal or nonterminal symbols. It can also have the production S → λ
as long as S does not appear on the right-hand side of any other
production.

Context Free Grammar:

grammar can have productions only of the form w1 → w2, where w1 is a
single symbol that is not a terminal symbol. A type 3 grammar can have
productions only of the form w1 → w2 with w1 = A and either w2 = aB or
w2 = a, where A and B are nonterminal symbols and a is a terminal
symbol, or with w1 = S and w2 = λ.

In my textbook, the author said : CSG is a special case of CFG. But, I don’t get this point. because in CSG, lAr -> lwr. l and r can be strings of zero or more terminal or nonterminal. So, when it is a string of zero (means : length = 0). we can write lAr as A. So, CSG will be CFG. So, CSG is CFG

Does something I have understand wrong ? Please correct it for me.

Thanks 🙂

Answer 1

The textbook is in error. As you say, a CFG is a special case of a CSG.

CSGs can express strictly more languages than CFGs can.