GATE CS 2021 Set 2 — Question 57
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MSQ+2 / -0HardRegular ExpressionsFinite Automata & Regular LanguagesTheory of Computation
Theory of Computation → Finite Automata & Regular Languages → Regular Expressions
Last updated
Question
Which of the following regular expressions represent(s) the set of all binary numbers that are divisible by three? Assume that the string is divisible by three.
Correct answer
(A) (0 + 1(01^ 0)^ 1)^; (B) (0 + 11 + 10(1 + 00)^ 01)^; (C) (0^ (1(01^ 0)^ 1)^)^
Solution
The DFA for binary numbers divisible by 3 has three states representing remainders 0, 1, and 2.
Option (B) is another valid representation of the same language, derived by considering different paths through the DFA.
Option (D) is incorrect as it fails to generate valid strings like (decimal 9).
- State (rem 0):
- State (rem 1):
- State (rem 2):
1.Eliminate : The path becomes a self-loop on with the label .
2.The resulting expression for the transition from back to via is .
3.Combined with the self-loop on , the full RE is . This matches option (A).
Option (C) is equivalent to (A) because . Option (B) is another valid representation of the same language, derived by considering different paths through the DFA.
Option (D) is incorrect as it fails to generate valid strings like (decimal 9).
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…