GATE CS 2014 Set 2 — Question 45
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumRecursive & RE LanguagesTuring Machines & ComputabilityTheory of ComputationRice's Theorem
Theory of Computation → Turing Machines & Computability → Recursive & RE Languages
Last updated
Question
Let be the encoding of a Turing machine as a string over . Let . Then, is
Correct answer
(B) undecidable but recursively enumerable
Solution
1.Undecidability: According to Rice's Theorem, any non-trivial property of the language recognized by a Turing machine is undecidable. The property "accepts a string of length 2014" is non-trivial because there exist Turing machines that accept such strings and others that do not. Therefore, is undecidable.
2.Recursively Enumerable (RE): A language is RE if there exists a Turing machine that accepts every string in the language and either rejects or loops for strings not in the language. We can construct a TM for that, given , simulates on all strings of length 2014 (there are finitely many: ) in a dovetailing manner. If accepts any of these strings, the simulator accepts . Thus, is recursively enumerable.
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 Turing Machines & Computability
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…