Explain removing unit productions in context free grammar

Data Structure Algorithms Computer Science Computers

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

Published on 16-Jun-2021 12:37:48

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