6.2 TWO IMPORTANT NORMAL FORMS

     CHOMSKY NORMAL FORM      GREIBACH NORMAL FORM

Edith Castro

March 27, 2014

Chomsky Normal Form

A context-free grammar is in Chomsky normal form if all productions are of the form:

A BC or A a

Where: A, B, C are variables and a is a terminal symbol.

Example 1:

Given the grammar: P: S AS | a,

A SA | b

The productions are of the Chomsky normal form.

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Chomsky Normal FormExample 2:

Given another grammar:

P: S AS | AAS,

A SA | aa

The productions S AAS and A aa do not follow the conditions of the Chomsky normal form. The grammar is not in the Chomsky normal form.

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Chomsky Normal Form

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Chomsky Normal Form

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Chomsky Normal Form

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Chomsky Normal Form

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Chomsky Normal Form

Example: Given the grammar with the productions:

S ABa, A aab,B Ac

Convert to Chomsky normal form.

Solution: We can apply the theorem 6.6. So the grammar does not have any - productions and no unit-productions.

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Chomsky Normal Form

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Chomsky Normal FormStep 1: We introduce additional variables to get the first two productions into normal form and we get the final result:

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