GATE CS 2020 Set 1 — Question 20
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Compiler Design → Context-Free Languages → DPDA vs NPDA
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Question
Consider the language and the following statements.I. is deterministic context-free.
II. is context-free but not deterministic context-free.
III. is not for any .Which of the above statements is/are TRUE?
II. is context-free but not deterministic context-free.
III. is not for any .Which of the above statements is/are TRUE?
Correct answer
(C) I and III only
Solution
Statement I is TRUE. The language is a Deterministic Context-Free Language (DCFL). A DPDA can be constructed that pushes 's onto the stack. If the input ends, it accepts (matching ). If a is encountered, it pops 's to match the count (matching ). Since the machine can make a deterministic decision based on the input (or lack thereof via final state acceptance), it is a DCFL.Statement II is FALSE because is DCFL.Statement III is TRUE. The language is inherently ambiguous in terms of parsing because for any lookahead , a string of 's could belong to either the part or the start of the part. The parser cannot decide which production to use (
S → A or S → B) with finite lookahead. Thus, it is not for any .Therefore, statements I and III are true.Continue learning with Success Tracker
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