GATE CS 2014 Set 3 — Question 46
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Theory of Computation → Context-Free Languages → DPDA vs NPDA
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Question
Consider the following languages over the alphabet :
Here, is the reverse of the string . Which of these languages are deterministic Context-free languages?
Here, is the reverse of the string . Which of these languages are deterministic Context-free languages?
Correct answer
(C) Only L₁ and L₂
Solution
Let's analyze each language:
1.: This is a standard Deterministic Context-Free Language (DCFL). A Deterministic Pushdown Automaton (DPDA) can push all 0s onto the stack and then pop one 0 for each 1 read. If the stack is empty exactly when the input ends, accept.
2.: This is also a DCFL. The character 'c' acts as a clear center marker. A DPDA can push the symbols of onto the stack. When 'c' is read, it transitions to a state that pops symbols from the stack and compares them with the remaining input . Since the transition is determined by the input symbol 'c', it is deterministic.
3.: This is a Context-Free Language (CFL) but not a DCFL. Without the center marker, the automaton has to "guess" where the middle of the string is to switch from pushing to popping/matching. This non-determinism cannot be removed for this specific language.
Thus, only and are deterministic context-free languages.Continue learning with Success Tracker
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