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Defining a CF language via derivation
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A string A derives a string B if
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A can be rewritten as B via some series of rule applications
More formally:
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If A -> ï¢ is a production of P
ï¡ and ï§ are any strings in the set (ï ï N)*
Then we say that
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Derivation is a generalization of direct derivation
Let ï¡1, ï¡2, ⦠ï¡m be strings in (ï ï N)*, m>= 1, s.t.
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ï¡Aï§ directly derives ï¡ï¢ï§ or ï¡Aï§ ï ï¡ï¢ï§
ï¡1ï ï¡2, ï¡2ï ï¡3⦠ï¡m-1ï ï¡m
We say that ï¡1derives ï¡m or ï¡1*ï ï¡m
We then formally define language LG generated by grammar G
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A set of strings composed of terminal symbols derived from S
LG = {w | w is in ï* and S *ï w}