GATE CS 2023 Set 1 — Question 39
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Theory of Computation → Context-Free Languages → Context-Free Grammars
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Question
Consider the context-free grammar belowwhere and are non-terminals, and and are terminal symbols. The starting non-terminal is .Which one of the following statements is CORRECT?
Correct answer
(B) The language generated by G is a^ (a + b)b^
Solution
1.Analyze non-terminal :
This grammar for is regular. It generates strings of the form where . Specifically, generates , which is equivalent to . This can be written as .
2.Analyze non-terminal :
This generates strings of the form for .
Let and . Since and :
- If , we can choose .
- If , we can choose .
- If , we can choose (so ).
L(G) consists of all strings such that . This is exactly the language , which is represented by the regular expression . Since the language is regular, option (D) is false and option (B) is correct.Continue learning with Success Tracker
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