GATE CS 2023 Set 1 — Question 40
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 Computation
Theory of Computation → Context-Free Languages → Pushdown Automata (PDA)
Last updated
Question
Consider the pushdown automaton (PDA) below, which runs on the input alphabet , has stack alphabet , and has three states , with being the start state. A transition from state to state , labelled , where is an input symbol or , is a stack symbol, and is a string of stack symbols, represents the fact that in state , the PDA can read from the input, with on the top of its stack, pop from the stack, push in the string on the stack, and go to state . In the initial configuration, the stack has only the symbol in it. The PDA accepts by empty stack.
Which one of the following options correctly describes the language accepted by ?
Correct answer
(A) \a^m bⁿ 1 ≤ m and n < m\
Solution
1.Analyze State : The transitions and push an 'A' for every 'a' read. Thus, after 'a's, the stack contains . Since there is no transition for or from when the stack is just , we must have .
2.Analyze Transitions to and :
- From , we can go to by reading a 'b' and popping an 'A' ().
- From , we can go directly to by popping an 'A' on input (). This corresponds to .
4.Analyze State : The transitions and allow emptying the stack completely.
5.Conclusion: The PDA accepts strings of the form where and .
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…