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Explain removing unit productions in context free grammar
All grammars are not always optimized, which means the grammar may consist of some extra symbols (non-terminals) which increase the length of grammar.
So, we have to reduce the grammar by removing the useless symbols.
Properties
The properties to reduce grammar are explained below −
- Each non-terminal and terminal of G appears in the derivation of some word in L.
- There should not be any production as X->Y where X and Y are non-terminals.
- If epsilon is not in language L then there need not be in the production X-> ε.
The diagram given herewith describe the properties to reduce grammar −
The unit productions are the productions in which one non-terminal gives another nonterminal
Remove unit production
The steps to remove the unit production are given below −
- Step 1 − To remove X->Y add production X->a to the grammar rule whenever Y->a occurs in the grammar.
- Step 2 − Now delete X->Y from the grammar
- Step 3 − Repeat Step 1 and 2 until all unit productions are removed
Example
Consider the context free grammar given below and remove unit production for the same.
S->0A|1B|C
A->0S|00
B->1|A
C->01
Explanation
Step 1
S->C is unit production but while removing S->C we have to consider what C gives so we can add a rule to S.
S->0A|1B|01
Step 2
B->A is also unit production
B->1|0S|00
Finally, we can write CFG without unit production as follows −
S->0A|1B|01
A->0S|00
B->1|0S|00
C->01
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