GATE CS 2016 Set 1 — Question 53
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumPushdown Automata (PDA)Context-Free LanguagesTheory of ComputationDPDA vs NPDA
Theory of Computation → Context-Free Languages → DPDA vs NPDA
Last updated
Question
Consider the transition diagram of a PDA given below with input alphabet and stack alphabet . is the initial stack symbol. Let denote the language accepted by the PDA.
Which one of the following is TRUE?
Correct answer
(D) L = \aⁿ n ≥ 0\ ∪ \aⁿ bⁿ n ≥ 0\ and is deterministic context-free
Solution
Read the PDA from the figure. It has three states: (start, accepting), , and (accepting). Acceptance is by final state.
- : and — every pushes one .
- : — the first pops one .
- : — every further pops one .
- : — possible only when all 's are gone.
- Since is accepting, any (, including ) is accepted while still in .
- A string reaches only if exactly 's are popped by the 's, i.e. .
- Any other string (a before an with an empty -stack, an after a , or ) gets stuck in a non-accepting configuration.
- (A) False: also contains for (e.g. ), so .
- (B) False: the language is correct, but the PDA shown is deterministic, so is accepted by a DPDA.
- (C) False: every CFL is decidable, so a halting Turing machine accepts .
- (D) True.
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE CS question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Context-Free Languages
2026 Set 2 Q13Which one of the following statements is equivalent to the following assertion? Turing machine …2026 Set 1 Q25Consider the following grammar where is the start symbol, and and are terminal symbols.…2026 Set 1 Q26Let be a nondeterministic finite automaton (NFA) with 6 states over a finite alphabet. Which of…2026 Set 2 Q29Which of the following grammars is/are ambiguous?2026 Set 2 Q47Consider the following two finite automata and . [figure] Which of the following…