Given a regular grammar G and a list of strings, identify the strings that are in L(G).
Transcribed Image Text:**Given Grammar G:**
- \( S \rightarrow aT \)
- \( T \rightarrow bT \)
- \( T \rightarrow a \)
- \( T \rightarrow aW \)
- \( W \rightarrow \varepsilon \)
- \( W \rightarrow aT \)
**Task:** List the first eight elements of \( L(G) \) in lexicographic order.
**Options:**
1.
- \( aa, \, aba, \, aaaa, \, abba, \, aaaba, \, abaaa, \, abbba, \, aaaaaa \)
2.
- \( ab, \, abb, \, aaab, \, abbb, \, aaabb, \, abaab, \, abbbb, \, aaaaab \)
3.
- \( ba, \, bba, \, baab, \, bbba, \, baaba, \, bbaaa, \, bbbaa, \, bbaaaa \)
4.
- \( bb, \, bba, \, bbaa, \, bbba, \, bbaba, \, bbbaa, \, bbbba, \, bbaaaa \)
In this exercise, you're asked to determine the correct sequence of strings generated by the given grammar in lexicographic order. The task involves understanding the production rules and deriving strings accurately.
Expert Solution
Step 1: Given
The given grammar G is:
S -> aT
T -> bT | a | aW
W -> ε | aT
This grammar generates strings that start with ‘a’ and can have any number of 'a’s or 'b’s following it. However, it cannot generate strings that start with ‘b’. Therefore, the options 3 and 4 are not possible with this grammar.
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