GATE CS 2020 Set 1 — Question 61
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+2 / -0MediumDFAFinite Automata & Regular LanguagesTheory of ComputationDFA Minimization
Theory of Computation → Finite Automata & Regular Languages → DFA
Last updated
Question
Consider the following language.
The minimum number of states in a DFA that accepts is ______.
The minimum number of states in a DFA that accepts is ______.
Correct answer
6 to 6
Solution
Let be the number of 's in string .
The condition for is:
So, the DFA needs to track the number of 's modulo 6. This requires 6 states: , where state represents .
The condition for is:
1.
2.
We track because . Let .So, the DFA needs to track the number of 's modulo 6. This requires 6 states: , where state represents .
- Transitions on 'a': .
- Transitions on 'b': (self-loops, as 'b' doesn't affect the count of 'a').
- Start state: .
- Final states: .
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 Finite Automata & Regular 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…