# What is context free grammar in automata theory ppt

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What does CFG do? There are two terminal symbols " " and " " and one nonterminal symbol S.

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### Context Free Grammars.

Are you sure you want to Yes No. Embeds 0 No embeds. No notes for slide. One piece of evidence is that they can all precede verbs. A grammar for English: Did the plane leave? A context-free grammar CFG is a collection of three things: A finite set of productions of the form: We require that at least one production has the nonterminal S as its left side. A set of symbols called nonterminals, one of which is the symbol S, standing for start here.

The language generated by a CFG is the set of all strings of terminals that can be produced from the start symbol S using the productions as substitutions. We insist that nonterminals be designated by capital letters, whereas terminals are designated by lowercase letters and special symbols.

If we apply Prod 1 six times and then apply Prod 2, we generate the following: The word ab can be generated by the derivation. The word baab can be generated by.

Clearly, the language generated by the above CFG is. Hence, the words generated from S have the form. For example, the word baabb can be generated by.

## Chomsky Classification of Grammars

For example, the word a4b4 is derived by. The language of G, denoted by L G is the set. We use this symbol to combine all the productions that have the same left side. For example, the CFG.

S and O work as counters i. Presence of O in a sentential form indicates that an odd number of terminals have been generated.

The strategy can be generalized, say for string of length exactly divisible by 3 we need three counters to mark 0, 1, 2. The non-terminals with interpretations are: In Chapter 16, we will see that there is some non-regular language that cannot be generated by any CFG. Thus, the set of languages generated by CFGs is properly larger than the set of regular languages, but properly smaller than the set of all possible languages.

We start with the symbol S. Every time we use a production to replace a nonterminal by a string, we draw downward lines from the nonterminal to EACH character in the string.

Reading from left to right produces the word bbaaaab.