Removal of Unit Production | Simplification of CFG | Elimination of Unit production | TOC
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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.
Unit productions – A unit production is a production A - B where both A and B are non-terminals. Unit productions are redundant and hence should be removed. Follow the following steps to remove the unit production
Repeat the following steps while there is a unit production
Select a unit production A - B, such that there exist a production B - α, where α is a terminal
For every non-unit production, B - α repeat the following step
Add production A - α to the grammar
Eliminate A - B from the grammar
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