Given grammar G:S->aS| ABA-> eB-> eD-> bReduce the grammar, removing all the e productions:ans.S->aS| AB| A| B, D-> bNone of the mentionedS->aS| AB| A| B| a, D-> bS->aS| AB| A| B 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, D-> bNone of the mentionedS->aS| AB| A| B| a, D-> bS->aS| AB| A| B Previous Marked for Review Next
Solution
The given grammar is:
G:
S -> aS | ABA
A -> e
B -> e
D -> b
The task is to reduce the grammar by removing all the epsilon (e) productions. Epsilon productions are the productions where a variable produces an empty string.
Step 1: Identify the nullable variables. A variable is nullable if it can generate an epsilon (e) production directly or indirectly. Here, A and B are nullable variables because they directly produce e.
Step 2: Remove the epsilon productions. The epsilon productions A -> e and B -> e are removed.
Step 3: For each production that contains nullable variables, add a new production where the nullable variable is removed. This step is done because the nullable variable can produce an empty string.
So, the reduced grammar becomes:
S -> aS | AB | A | B
D -> b
Note: The production S -> aS | AB | A | B means that S can produce aS, AB, A, or B. Similarly, D -> b means that D can produce b.
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