Topic10- Type of Grammar

8/3/2019 Topic10- Type of Grammar

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Type of Phrase Structure Grammar


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Unrestricted Grammar (Type 0)

A grammar G = (V, T, S, P) is unrestrictedif it has no conditions are imposed on theproductions, which are of the form x y,

where x

(V

T)

+

and y

(V

T)* a combination of one or more vocabulary

denoted by xcan be replaced by acombination of zero or more vocabulary

denoted by y Exception: does not appear on the left side

of a production


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Context-sensitive Grammar (Type 1)

A grammar G = (V, T, S, P) is context-sensitive if everyproduction is of the form pAq pyq, where A V; p, q

(VT)* and y (VT)+

a variable Aoccurring in the context of string ponthe left and qon the right can be replaced by acombination of one or more vocabulary denoted by y

the substitution of the variable on the left of aproduction is context sensitive, i.e., A y

does not appear on both the left and right side of a

production; so,G cannot generate a languagecontaining null string

therefore, the derivation is non-contracting, i.e.,| pAq| | pyq|


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Context-free Grammar (Type 2)

A grammar G = (V, T, S, P) is context-free

if every production is of the form A y; A

V and y (VT)*

a singlevariable Acan be replaced by a

combination of zero or more vocabularydenoted by y

the substitution of the variable on the left of a

production is context insensitive, i.e., it doesnot depend upon the rest of the symbols inthe string


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Regular Grammar (Type 3) A grammar G = (V, T, S, P) is a regular grammar if every

production is of the form:

A xB(c.f. Grammar Type 2)A xA

where A, BV and xT

Note that A, Bare variables, and xis strictly a singleterminal symbol

is a context-free grammar

e.g. G = ({S, A}, {a,b}, S, {S bA | a | , A aA | bA | b})

Regular grammar is concise way to describe a formallanguage


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Classification by Noam Chomsky

A grammar that has no restriction on itsproduction is called type-0 grammar

A grammar in which every production is ofthe form |w1| |w2| or the form w1, iscalled type-1 grammar.

A grammar in which every production is of

the form w1w2, where w1 is a single non-terminal, is called type-2 grammar


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Classification by Noam Chomsky

A grammar in which every production is ofthe form w1w2, where w1 is a single non-terminal symbol and w2 is a single terminalor a terminal followed by a non-terminal orof the form S, called type-3 grammar ora regular grammar.

From the definition given, it is obious that every

type-3 grammar is a type-2 grammar,every type-2 grammar is a type-1 grammar andevery type-1 grammar is a type-0 grammar.


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Phrase Structure Grammar

Phrase structure grammar can also beclassified according to another criteria asfollows:


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Backus-Naur Form(BNF)


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Topic10- Type of Grammar

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