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Explain type 2 grammar with properties
Type 2 grammars are context free grammars (CFG).
All productions are of the form −
A → x — where A is nonterminal, x is a string of nonterminal and terminals,
A context-free grammar is equivalent to a pushdown automaton (PDA) and to context free languages.
Example − Pushdown Automaton (PDA)
Properties
A grammars, G = (V, T, P, S) is said to be context free if the production rule is of the form, A → α .
The transition allows A → ε [i.e., α → ε] where, A is a non terminal symbol α is any terminal or non-terminal symbol.
Here, the left hand side of the transition rule consists of only one non-terminal.
Type 2 grammars are the basis of the syntax of most programming languages such as XML. Properties
The CFG is closed under the following −
Union
Concatenation
Kleene closure
It is not closed under complementation, substitution, reversal.
Example
Consider the production, P ⇒ {S → aSa, S → bSb, S → ε}
Since S → aSa → aaSaa [as S → aSa] → aabSbaa [as S → bSb] → aabbaa [as S → ε]
Thus, S may generate S = {ε, aa, bb, abba, aabbaa, abaaba, …}
Thus, the language is defined as L(G) = {w wR | w ε {a, b}*}
CFG can be handled using the pushdown automaton that uses stack memory to store the symbols.
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