Given grammar G:S->aS| ABA-> eB-> eD-> bReduce the grammar, removing all the e productions:ans.S->aS| AB| A| B| a, D-> bS->aS| AB| A| BS->aS| AB| A| B, D-> bNone of the mentioned Previous Marked for Review Next
Question
Given grammar G:S->aS| ABA-> eB-> eD-> bReduce the grammar, removing all the e productions:ans.S->aS| AB| A| B| a, D-> bS->aS| AB| A| BS->aS| AB| A| B, D-> bNone of the mentioned Previous Marked for Review Next
Solution
The given grammar is:
G:
S -> aS | AB
A -> e
B -> e
D -> b
The task is to remove all the e (epsilon) productions. Epsilon productions are the productions where a variable is directly producing an epsilon.
Step 1: Identify the nullable variables. A nullable variable is a variable that can generate an epsilon. Here, A and B are nullable variables because they directly produce an epsilon.
Step 2: For each production rule, generate new rules by removing the nullable variables in all possible ways.
The new set of production rules after removing the epsilon productions is:
S -> aS | AB | aS | a
A ->
B ->
D -> b
Note: The production rules A -> and B -> are not valid as they do not produce anything. They are included here for completeness and to show that A and B do not produce anything after removing the epsilon productions.
So, the reduced grammar is:
S -> aS | AB | aS | a
D -> b
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