Removal of Null Production | Simplification of CFG | Elimination of Epsilon production | TOC

#removalofnullproduction, #nullproductionremoval, #gatecs, #thegatehub
The definition of context free grammars (CFGs) allows us to develop a wide variety of grammars. Most of the time, some of the productions of CFGs are not useful and are redundant. This happens because the definition of CFGs does not restrict us from making these redundant productions.
By simplifying CFGs we remove all these redundant productions from a grammar , while keeping the transformed grammar equivalent to the original grammar. Two grammars are called equivalent if they produce the same language. Simplifying CFGs is necessary to later convert them into Normal forms.
NULL productions – The productions of type ‘A - NULL’ are called NULL productions ( also called lambda productions and null productions) . These productions can only be removed from those grammars that do not generate λ (an empty string). It is possible for a grammar to contain null productions and yet not produce an empty string.
To remove null productions , we first have to find all the nullable variables. A variable ‘A’ is called nullable if NULL can be derived from ‘A’. For all the productions of type ‘A - NULL’ , ‘A’ is a nullable variable. For all the productions of type ‘B - A1A2…An ‘ , where all ’Ai’s are nullable variables , ‘B’ is also a nullable variable.

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