GATE CS 2017 Set 2 — Question 40
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Theory of Computation → Context-Free Languages → Context-Free Grammars
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Question
Consider the following languages.
Which of the following are CORRECT?I. is context-free but not regular.
II. is not context-free.
III. is not context-free but recursive.
IV. is deterministic context-free.
Which of the following are CORRECT?I. is context-free but not regular.
II. is not context-free.
III. is not context-free but recursive.
IV. is deterministic context-free.
Correct answer
(D) III and IV only
Solution
Step-by-step analysis of the statements:
1.Statement I: is a standard example of a language that is not context-free (it is a Context-Sensitive Language). Thus, I is incorrect.
2.Statement II: can be written as . Since is regular and is context-free (requires one comparison), their concatenation is context-free. Thus, II is incorrect.
3.Statement III: requires two simultaneous comparisons ( of 's with of 's, and of 's with of 's), which a single stack cannot do. It is not context-free but is recursive (it's a CSL). Thus, III is correct.
4.Statement III: is a standard Deterministic Context-Free Language (DCFL) as it can be accepted by a Deterministic Pushdown Automaton. Thus, IV is correct.
Statements III and IV are correct, which corresponds to option (D).Continue learning with Success Tracker
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