Removal of Useless Production | Simplification of CFG | Elimination of Useless production | TOC

#removalofuselessproduction, #uselessproductionremoval, #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.
In this tutorial we define those symbols that do not participate in derivation of any string, i.e. the useless symbols, and remove the useless productions from the grammar.
A symbol X is useful if:
If X is generating, i.e., X =* w, where w ϵ L(G) and w in Vt*, this means that the string leads to a string of terminal symbols.
If X is reachable If there is a derivation S =* αXβ =* w, w ϵ L(G), for same α and β, then X is said to be reachable.
A number that is useful is both generating and reachable. For reduction of a given grammar G:
Identify non-generating symbols in the given CFG and eliminate those productions which contains non-generating symbols.
Identify non-reachable symbols and eliminate those productions which contain the non-reachable symbols

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